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THE UNIVERSAL DUAL COMODULE OF MODULE IN HOPF ALGEBRAS 被引量:1
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作者 郝志峰 冯良贵 《Acta Mathematica Scientia》 SCIE CSCD 2003年第3期289-296,共8页
The purpose of this paper is to present some dual properties of dual comodule. It turns out that dual comodule has universal property (cf.Theorem 2). Since (( )*,()°) is an adjoint pair (cf.Theorem 3), some nice ... The purpose of this paper is to present some dual properties of dual comodule. It turns out that dual comodule has universal property (cf.Theorem 2). Since (( )*,()°) is an adjoint pair (cf.Theorem 3), some nice properties of functor ( )° are obtained. Finally Theoram 4 provides that the cotensor product is the dual of the tensor product by (M (?)A N)°≌M°□A°N°. Moreover, the result Hom(M,JV)≌ComA°(N°,M°) is proved for finite related modules M, N over a reflexive algebra A. 展开更多
关键词 Universal dual comodule Hopf algebras cotensor product adjoint pair
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QUANTUM COMODULE APPROACH THE SOLUTION OF THE QUANTUM YANG-BAXTER EQUATION
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作者 李立斌 李尚志 《Acta Mathematica Scientia》 SCIE CSCD 2000年第2期206-212,共7页
In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible ... In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible to give some set-theoretical solutions of the Quantum Yang-Baxter Equation. 展开更多
关键词 Quantum Yang-Baxter Equation quantum comodule SOLUTION Hopf algebra
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Some remarks on cotilting comodules 被引量:2
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作者 Sujuan ZHANG Hailou YAO 《Frontiers of Mathematics in China》 SCIE CSCD 2014年第3期699-714,共16页
We study cotilting comodules and f-cotilting comodules and give a description of localization of f-cotilting comodules and classical tilting comodules. First, we introduce T-cotilting injective comodules and their dim... We study cotilting comodules and f-cotilting comodules and give a description of localization of f-cotilting comodules and classical tilting comodules. First, we introduce T-cotilting injective comodules and their dimensions which are important for researching cotilting comodules. Then we characterize the localization in f-cotilting comodules, finitely copresented comodules, and classical tilting comodules. In particular, we obtain a localizing property about finitely copresented comodules. 展开更多
关键词 COALGEBRA comodule LOCALIZATION
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A Duality Theorem for Hopf Comodule Coalgebras 被引量:1
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作者 王栓宏 《Chinese Science Bulletin》 SCIE EI CAS 1994年第15期1239-1244,共6页
R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the con... R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the concept of Hopf comodule coalgebras which is a dual notation of Hopf module algebra, and discussed their properties. However, the duality theorem of Hopf comodule coalgebras has not been proved yet. In this note we shall deal with this situation by defining the 展开更多
关键词 HOPF ALGEBRA HOPF comodule COALGEBRA HOPF module COALGEBRA SMASH coproduct.
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Morita theorems for Hopf comodule coalgebras
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作者 刘贵龙 《Chinese Science Bulletin》 SCIE EI CAS 1996年第12期969-972,共4页
Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#... Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#H] under the additional assumption thatH was unimodular and used the Morita context to study the Smash product A#H. In1990, Cohen, Fischman and Montgomery showed that fix ring A^H and smash product 展开更多
关键词 pre-equivalence DATE HOPF comodule COALGEBRA HOPF module coalgebra.
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Decomposition of Comodules
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作者 邹小贵 许永华 《Science China Mathematics》 SCIE 1994年第8期946-953,共8页
It has been proved, using a special approach, that any comodules over a field can be uniquely decomposed into the direct sum of closed indecomposable subcomodules.
关键词 COALGEBRA comodule coradical WEDGE product.
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Relation between decomposition of comodules and coalgebras
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作者 张寿传 《Science China Mathematics》 SCIE 1997年第1期24-29,共6页
Let M be a C-comodule. It is clear that M and C can both be decomposed into a direct sum of the indecomposable subcoalgebras of C and subcomodules of M. The relation between the two decompositions is given
关键词 COALGEBRA comodule comodule component decomposition.
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Lie comodules and the constructions of Lie bialgebras
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作者 ZHANG LiangYun College of Science,Nanjing Agricultural University,Nanjing 210095,China 《Science China Mathematics》 SCIE 2008年第6期1017-1026,共10页
In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras.
关键词 Lie coalgebras Lie comodules Lie bialgebras triangular Lie bialgebras 16W30
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HOPF-JACOBSON RADICAL FOR COMODULE ALGEBRAS
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作者 CAICHUANREN GUOGUANGQUAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1999年第2期261-270,共10页
Let H be a Hop f algebra over a field k (not necessarily finite dimensional). In this paper theHopf-Jacobson radical JH(A) of right H-comodule algebra A (not necessarily with identity)is studied. The relationships bet... Let H be a Hop f algebra over a field k (not necessarily finite dimensional). In this paper theHopf-Jacobson radical JH(A) of right H-comodule algebra A (not necessarily with identity)is studied. The relationships between JH(A) and the Jacobson radical of the smash productA#H*,", are discussed. The density theorem is given for left (A, H)-Hopf simple module. 展开更多
关键词 comodule algebra Hopf-Jacobson radical Density theorem
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Equivalences between Categories of Modules and Categories of Comodules
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作者 Joost VERCRUYSSE 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第10期1655-1674,共20页
We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gomez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Re... We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gomez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Represent. Theory, 10 (2007), 271 306] and [Wisbauer, On Galois comodules, Comm. Algebra 34 (2006), 2683-2711]. Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring. We show that these equivalences are related to Galois theory for comodules. 展开更多
关键词 Galois comodules comatrix corings firm projectivity
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Duality theorem for smash coproduct over quantum groupoids
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作者 周璇 刘玲 王栓宏 《Journal of Southeast University(English Edition)》 EI CAS 2010年第4期647-650,共4页
The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left... The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC(C,H)and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,(C×lH H)×lH H≌Cv(H×lH H),is obtained. 展开更多
关键词 weak Hopf algebras(quantum groupoids) weak generalized smash coproducts weak module coalgebras weak comodule coalgebras weak bimodule coalgebras duality theorem
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The Structure Theorem for Module Coalgebras
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作者 WANG Yong ZHANG Liang-yun CAI Zhi-min 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期85-92,共8页
This paper,mainly gives the structure theorem for module coalgebras by a kind of new method,and deletes the condition that the antipode S of the Hopf algebra H is bijective.
关键词 Hopf algebra Hopf bicomodule comodule coalgebra smash coproduct module coalgebra
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Recent Developments in Morita Equivalence: Part Two
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作者 汪明义 《Journal of Modern Transportation》 2000年第1期4-12,共9页
Morita equivalence was established by Morita in the late 1950’s. In part one most of the recent developments in this theory on the categories of modules over rings were reviewed and some results were presented. Here ... Morita equivalence was established by Morita in the late 1950’s. In part one most of the recent developments in this theory on the categories of modules over rings were reviewed and some results were presented. Here this paper discusses those on categories of comodules over coalgebras, these results are due to Ling, Takeuchi and Wang. 展开更多
关键词 Morita equivalence Morita Takeuchi equivalence COALGEBRAS categories of comodules QcF coalgebras classical tilting comodules
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THE FIELD ALGEBRA IN HOPF SPIN MODELS DETERMINED BY A HOPF*-SUBALGEBRA AND ITS SYMMETRIC STRUCTURE
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作者 Xiaomin WEI Lining JIANG Qiaoling XIN 《Acta Mathematica Scientia》 SCIE CSCD 2021年第3期907-924,共18页
Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More... Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More precisely, we consider the quantum double D(H, H_(1)) as the bicrossed product of the opposite dual Hopˆ of H and H1 with respect to the coadjoint representation, the latter acting on the former and vice versa, and under the non-trivial commutation relations between H1 and Ĥ we define the observable algebra AH1. Then using a comodule action of D(H, H1) on AH1, we obtain the field algebra FH1, which is the crossed product AH1⋊D(H,H_(1)), and show that the observable algebra AH1 is exactly a D(H, H1)-invariant subalgebra of FH1. Furthermore, we prove that there exists a duality between D(H, H1) and AH1, implemented by a*-homomorphism of D(H, H_(1)). 展开更多
关键词 comodule algebra field algebra observable algebra COMMUTANT duality
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Group Twisted Tensor Bipro ducts over Hopf Group Coalgebras
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作者 CHEN Quan-guo TANG Jian-gang 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第2期274-282,共9页
In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and su?cient conditions for the new object to be a Hopf group coalgebra.
关键词 Hopf group coalgebra twisted tensor biproduct comodule coalgebra
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On the Structure of the B-cocleft Module Coalgebra
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作者 焦争鸣 王栓宏 赵文正 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第4期44-47, ,共4页
In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is ... In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras. 展开更多
关键词 H module coalgebra H weakly comodule coalgebra crossed coproduct
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The tensor algebras of Yetter-Drinfeld module
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作者 Yanhua Wang 《上海师范大学学报(自然科学版)》 2014年第5期523-528,共6页
The antipode of a Yetter-Drinfeld Hopf algebra is an anti-algebra and anti-coalgebra map is proved. It is also proved that the tensor algebra of Yetter-Drinfeld Hopf module is a Yetter-Drinfeld Hopf algebra.
关键词 Hopf algebra ANTIPODE comodule Yetter-Drinfeld Hopf algebras
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A duality theorem of crossed coproduct for Hopf algebras 被引量:4
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作者 王栓宏 《Science China Mathematics》 SCIE 1995年第1期1-7,共7页
A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).
关键词 HOPF ALGEBRAS H-weak comodule COALGEBRA CROSSED coproduct.
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(*)-Serial coalgebras 被引量:1
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作者 Hailou YAO Weili FAN Yanru PING 《Frontiers of Mathematics in China》 SCIE CSCD 2012年第5期955-970,共16页
In this paper, we introduce the notion of (*)-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of (*)-serial coalgebras and their comodules, and obtain sufficient a... In this paper, we introduce the notion of (*)-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of (*)-serial coalgebras and their comodules, and obtain sufficient and necessary conditions for a basic coalgebra to be (*)-serial. 展开更多
关键词 COALGEBRA biserial comodule )-serial coalgebra QUIVER
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Morita contexts on the Hopf algebroid
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作者 YIN Yanmin School of Mathematical Sciences, Peking University, Beijing 100871, China Department of Mathematics, Shandong Institute of Architecture and Engineering, Jinan 250101, China 《Science China Mathematics》 SCIE 2005年第7期958-971,共14页
We generalize the Morita theory to the Hopf algebroid and give the characterization of the surjectivity of one of the Morita context maps.
关键词 comodule algebra GENERALIZED SMASH product MORITA context.
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