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Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras
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作者 CHEN Zheng-xin WANG Bing 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第4期516-522,共7页
A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgeb... A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P. 展开更多
关键词 commuting maps finite-dimensional simple lie algebras standard parabolic subalgebras
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Co-splitting of Simple Lie Algebras of Type A, D, E
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作者 Zhao Yu-e Du Xian-kun 《Communications in Mathematical Research》 CSCD 2015年第3期229-241,共13页
In this paper, through a meticulous description of finite root system,a concrete comultiplication with an explicit action on the basis elements of finitedimensional simple Lie algebras of type A; D; E is constructed. ... In this paper, through a meticulous description of finite root system,a concrete comultiplication with an explicit action on the basis elements of finitedimensional simple Lie algebras of type A; D; E is constructed. Then any finitedimensional simple Lie algebra of type A; D; E is endowed with a new generalizedLie coalgebra splitting. This construction verifies the known existence of a co-splitLie structure on any finite dimensional complex simple Lie algebra. 展开更多
关键词 lie coalgebra co-splitting finite-dimensional simple lie algebra
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Non-linear Maps on Borel Subalgebras of Simple Lie Algebras Preserving Abelin Ideals
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作者 赵延霞 王登银 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期615-623,共9页
Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In ... Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь. 展开更多
关键词 simple lie algebra abelian ideal non-linear map
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A class of simple Lie algebras attached to unit forms 被引量:1
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作者 Jinjing CHEN Zhengxin CHEN 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第4期787-803,共17页
Abstract Let n ≥ 3. The complex Lie algebra, which is attached to a unit form xixj and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A~, and r... Abstract Let n ≥ 3. The complex Lie algebra, which is attached to a unit form xixj and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A~, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra. 展开更多
关键词 Nakayama algebras finite-dimensional simple lie algebras Ringel-Hall lie Mgebras
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Simple algebras of Weyl type 被引量:3
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作者 苏育才 赵开明 《Science China Mathematics》 SCIE 2001年第4期419-426,共8页
Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A?F[D] from any pair of a commutative associative algebra,A with an identity element... Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A?F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras. 展开更多
关键词 simple lie algebra simple associative algebra DERIVATION
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A Class of Non-degenerate Solvable Lie Algebras and Their Derivations 被引量:1
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作者 Hai Shan ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第1期7-16,共10页
The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.
关键词 non-degenerate SOLVABLE DERIVATION finite-dimensional simple lie algebra
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A New Functor from D_5-Mod to E_6-Mod
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作者 Xiao Ping XU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第8期867-892,共26页
We find a new representation of the simple Lie algebra of type E6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this r... We find a new representation of the simple Lie algebra of type E6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen's idea of mixed product, we construct a new functor from Ds-Mod to E6-Mod. A condition for the functor to map a finite-dimensional irreducible Ds-module to an infinite-dimensional irreducible E6-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant's characteristic identities plays a key role. 展开更多
关键词 simple lie algebra of type E6 simple lie algebra of type Ds module category functor irreducibility
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Partial Differential Equation Approach to E_7
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作者 Xiao Ping XU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第2期177-200,共24页
By solving certain partial differential equations, we find the explicit decomposition of the polynomial algebra over the 56-dimensional basic irreducible module of the simple Lie algebra E7 into a sum of irreducible s... By solving certain partial differential equations, we find the explicit decomposition of the polynomial algebra over the 56-dimensional basic irreducible module of the simple Lie algebra E7 into a sum of irreducible submodules. This essentially gives a partial differential equation proof of a combinatorial identity on the dimensions of certain irreducible modules of E7. We also determine two three-parameter families of irreducible submodules in the solution space of Cartan's well-known fourth-order Ez-invariant partial differential equation. 展开更多
关键词 simple lie algebra E7 partial differential equation irreducible module decomposition combinatorial identity
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A New Multiplicity Formula for the Weyl Modules of Type B and C
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作者 Jia Chen YE Ben Sheng YUN Jia ZHAN 《Journal of Mathematical Research and Exposition》 CSCD 2010年第4期675-686,共12页
A monomial basis and a filtration of subalgebras for the universal enveloping algebra U(gl) of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V (λ) as a U(g... A monomial basis and a filtration of subalgebras for the universal enveloping algebra U(gl) of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V (λ) as a U(gl)-module into a direct sum of Weyl modules V (μ)’s as U(gl-1)modules is described. In particular, a new multiplicity formula for the Weyl module V (λ) is obtained in this note. 展开更多
关键词 simple lie algebra multiplicity formula WEIGHT irreducible module.
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Conjugation in Representations of the Zassenhaus Algebra
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作者 Bin SHU Institute of Applied Mathematics & Physics. Shanghai Maritime University. Shanghai 200135, P. R. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2001年第2期319-326,共8页
Let F be an algebracially closed field of characteristic p】2, and L be the p<sup>n</sup>-dimensional Zassenhaus algebra with the maximal invariant subalgebra L<sub>0</sub> and the standard fil... Let F be an algebracially closed field of characteristic p】2, and L be the p<sup>n</sup>-dimensional Zassenhaus algebra with the maximal invariant subalgebra L<sub>0</sub> and the standard filtration {L<sub>i</sub>}|<sub>i=-1</sub><sup>p<sup>n</sup>-2</sup>. Then the number of isomorphism classes of simple L-modules is equal to that of simple L<sub>0</sub>-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than p<sup>n</sup>. 展开更多
关键词 Zassenhaus algebras (Cartan-type lie algebras) simple modules of lie algebras and their isomorphism classes
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