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COMPLETELY BOUNDED COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS 被引量:1
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作者 侯成军 魏翠萍 《Acta Mathematica Scientia》 SCIE CSCD 2007年第1期25-33,共9页
The authors prove that all n-th completely bounded cohomology groups of a nest algebra T(N) acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T(N)-bimodule contain... The authors prove that all n-th completely bounded cohomology groups of a nest algebra T(N) acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T(N)-bimodule containing the nest algebra. They also prove that Hcb^n(A, M) ≌ Hcb^n(A, M) for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A. 展开更多
关键词 Nest algebra CSL algebra completely bounded cohomology group
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Two Kinds of Solvable Complete Lie Algebras 被引量:1
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作者 朱林生 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第3期59-66,共8页
In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nil... In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras. 展开更多
关键词 complete Lie algebra Heisenberg algebra abclian reqular quadratic Lie algebra
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A Note on Complete Color Lie Superalgebras
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作者 周建华 《Journal of Southeast University(English Edition)》 EI CAS 1997年第2期112-115,共4页
We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.
关键词 derivation complete algebra COLOR LIE SUPERalgebra
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Completely Positive Definite Maps Over Topological-algebras
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作者 许天周 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第4期73-77, ,共5页
In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definit... In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definite maps over topological algebras are given. 展开更多
关键词 topological algebra n-positive definite maps completely positive definite map schwarz type inequality Stinespring representation theorem
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Elementary n-Lie Algebras 被引量:2
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作者 白瑞蒲 张艳艳 《Northeastern Mathematical Journal》 CSCD 2007年第4期321-334,共14页
In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras. We also give the relations between elementary n-algebras a... In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras. We also give the relations between elementary n-algebras and E-algebras. 展开更多
关键词 Frattini subalgebra elementary n-lie algebra E-algebra
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Frattini Subalgebras and Nonimbedding Theorem of n-Lie Algebras 被引量:1
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作者 白瑞蒲 周和月 刘学文 《Northeastern Mathematical Journal》 CSCD 2006年第4期425-432,共8页
In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalg... In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalgebras of n-Lie algebras over the field with characteristic zero, and prove that the Frattini subalgebra of any k-solvable (k ≥2) n-Lie algebra is zero. 展开更多
关键词 n-lie algebra Frattini subalgebra lower central series
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THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA
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作者 周惊雷 李庆国 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期810-818,共9页
Let (L, 〈, V, A) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively... Let (L, 〈, V, A) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain: (i) the necessary and sufficient conditions for S(A,b)≠Ф; (ii) the necessary conditions for IS(A,b)| = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S(A, b) if S(A, b)≠Ф. 展开更多
关键词 complete lattice Heyting algebra linear system minimal covering
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Deducing Complete Selection Rule Set for Driver Nodes to Guarantee Network’s Structural Controllability 被引量:4
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作者 Xichen Wang Yugeng Xi +1 位作者 Wenzhen Huang Shuai Jia 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第5期1152-1165,共14页
Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make ... Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make the network structurally controllable. Different from the works in complex network field where structural controllability is often used to explore the emergence properties of complex networks at a macro level,in this paper, we investigate it for control design purpose at the application level and focus on describing and obtaining the solution space for all selections of driver nodes to guarantee structural controllability. In accord with practical applications,we define the complete selection rule set as the solution space which is composed of a series of selection rules expressed by intuitive algebraic forms. It explicitly indicates which nodes must be controlled and how many nodes need to be controlled in a node set and thus is particularly helpful for freely selecting driver nodes. Based on two algebraic criteria of structural controllability, we separately develop an input-connectivity algorithm and a relevancy algorithm to deduce selection rules for driver nodes. In order to reduce the computational complexity,we propose a pretreatment algorithm to reduce the scale of network's structural matrix efficiently, and a rearrangement algorithm to partition the matrix into several smaller ones. A general procedure is proposed to get the complete selection rule set for driver nodes which guarantee network's structural controllability. Simulation tests with efficiency analysis of the proposed algorithms are given and the result of applying the proposed procedure to some real networks is also shown, and these all indicate the validity of the proposed procedure. 展开更多
关键词 algebraIC criteria complete SELECTION rule set structural CONTROLLABILITY DRIVER NODES
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The Lie Algebras in which Every Subspace Is Its Subalgebra 被引量:1
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作者 Wu MING-ZHONG Liu Jian-ya 《Communications in Mathematical Research》 CSCD 2009年第1期1-8,共8页
In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, ... In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete. 展开更多
关键词 HB Lie algebra complete Lie algebra HOLOMORPH
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On the Model Properties of BCK Algebras
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作者 LIANGJun-qi 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期300-305,共6页
This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model... This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model complete, and hence there exist no built-in Skolem function. Moreover, the ultraproduct BCK algebras and the fuzzy ultraproduct of fuzzy subsets of BCK algebras were proposed by using the concept of ultrafilters with corresponding properties of fuzzy ideals discussed. 展开更多
关键词 BCK algebra mode complete complete ULTRAPRODUCT fuzzy ultraproduct
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The Realization of 4-dimensional 3-Lie Algebras
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作者 刘建波 张艳艳 张知学 《Northeastern Mathematical Journal》 CSCD 2007年第3期247-254,共8页
In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and ... In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras. 展开更多
关键词 4-dimensional 3-Lie algebra REALIZATION semi-simple n-lie algebra
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The Mathematical and Physical Theory of Rational Human Intelligence: Complete Empirical-Digital Properties;Full Electrochemical-Mechanical Model (Part I: Mathematical Foundations)
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作者 Leo Depuydt 《Advances in Pure Mathematics》 2013年第5期491-561,共71页
The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is stric... The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is strictly digital—not quantitative in the manner that what is usually thought of as mathematics is quantitative. It is anticipated at this time that the exclusively digital nature of rational human intelligence exhibits four flavors of digitality, apparently no more, and that each flavor will require a lengthy study in its own right. (For more information,please refer to the PDF.) 展开更多
关键词 Artificial INTELLIGENCE Boolean algebra Boole’s algebra Black Box Theories Brain Science Cognition Cognitive Science Digital MATHEMATICS Electricity and Magnetism J.-L. Lagrange and Partial Differential Equations J. C. Maxwell’s Theory of Electromagnetism Neuroscience Non-Quantitative and Quantitative MATHEMATICS Physics RATIONAL Human INTELLIGENCE complete Theory of RATIONAL Thought and Language
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The Automorphism Groups of Complete Lie Algebras with Commutative Nilpotent Radical
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作者 杨国庆 《Journal of Mathematical Research and Exposition》 CSCD 1999年第4期641-645,共5页
The automorphism groups of finite-dimensional complete Lie algebras withcommutative nilpotent radical over complex field C are given.
关键词 nilpotent. radical complete Lie algebra automorphism groups.
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Bi-Frobenius Algebra Structures on Quantum Complete Intersections
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作者 Hai JIN Pu ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第6期1481-1504,共24页
This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field k.We find a class of comultiplications,such that if√−1∈k,then a quantum complete intersection becomes a bi-Frobe... This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field k.We find a class of comultiplications,such that if√−1∈k,then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters qij=±1.Also,it is proved that if√−1∈k then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter q=±√1.While if−1/∈k,then the exterior algebra with two variables admits no bi-Frobenius algebra structures.We prove that the quantum complete intersections admit a bialgebra structure if and only if it admits a Hopf algebra structure,if and only if it is commutative,the characteristic of k is a prime p,and every ai a power of p.This also provides a large class of examples of bi-Frobenius algebras which are not bialgebras(and hence not Hopf algebras).In commutative case,other two comultiplications on complete intersection rings are given,such that they admit non-isomorphic bi-Frobenius algebra structures. 展开更多
关键词 Bi-Frobenius algebras COalgebras BIalgebras Hopf algebras quantum complete intersections quantum exterior algebras
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Extended Fan's Algebraic Method and Its Application to KdV and Variant Boussinesq Equations 被引量:7
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作者 YANG Xian-Lin TANG Jia-Shi College of Mechanics and Aerospace,Hunan University,Changsha 410082,China2 Department of Computer Science,Hunan Radio and Television University,Changsha 410004,China 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第7期1-6,共6页
An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential e... An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions. 展开更多
关键词 algebraic method KdV equation variant boussinesq equations polynomial complete discrimination system
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Complete Lie algebras with maximal-rank nilpotent radicals 被引量:2
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作者 ZHU Linsheng and MENG Daoji Department of Mathematics, Changshu College , Changshu 215500, China Department of Mathematics, Nankai University, Tianjin 300071, China 《Chinese Science Bulletin》 SCIE EI CAS 1999年第4期312-315,共4页
Ccmplete Lie algebras with maximal-rank nilpotent radicals are constructed by using the representation theory of complex semisimple Lie algebras. A structure theorem and an isomorphism theorem for this kind of complet... Ccmplete Lie algebras with maximal-rank nilpotent radicals are constructed by using the representation theory of complex semisimple Lie algebras. A structure theorem and an isomorphism theorem for this kind of complete Lie algebras are obtained. As an application of these theorems, the complete Lie algebras with abelian nilpotont radicals are classified. At last, it is proved that there exists no complete Lie algebra whose radical is a nilpotent Lie algebra with maximal rank. 展开更多
关键词 complete LIE algebra NILPOTENT LIE algebra with MAXIMAL RANK IRREDUCIBLE module.
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COMPLETE LIE ALGEBRAS WITH l-STEP NILPOTENT RADICALS 被引量:3
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作者 GAOYONGCUN MENGDAOJI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2002年第4期545-550,共6页
The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by... The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals. 展开更多
关键词 complete Lie algebra l-step nilpotent Lie algebra Nilpotent radical
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Complete Lie algebras
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作者 MENG DaojiDepartment of Mathematics , Nankai University, Tianjin 300071, China 《Chinese Science Bulletin》 SCIE EI CAS 1999年第11期961-964,共4页
A remark on complete Lie algebras is given. Since the theory of complete Lie algebras is still developing, this remark cannot be complete.
关键词 complete LIE algebra DERIVATION center.
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Derivation Algebra of Quasi R_n-filiform Lie Algebra
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作者 Wu MING-EHONG 《Communications in Mathematical Research》 CSCD 2012年第3期218-224,共7页
In this paper we explicitly determine the derivation algebra of a quasi Rn-filiform Lie algebra and prove that a quasi Rn-filiform Lie algebra is a completable nilpotent Lie algebra.
关键词 filiform Lie algebra complete Lie algebra derivation algebra
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Solvable complete Lie algebras (I)
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作者 孟道骥 朱林生 《Chinese Science Bulletin》 SCIE EI CAS 1996年第15期1317-1318,共2页
Let N be a nilpotent Lie algebra. An abelian subalgebra of DerN, whose elements are semisimple linear transformations of N, is called a torus on N. The dimension of a maximal torus H on N is called the rank of N.
关键词 Solvable complete Lie algebras
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