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Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems
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作者 Marina Tvalavadze 《Algebra Colloquium》 SCIE CSCD 2015年第2期281-292,共12页
In this work we axe concerned with the universal associative envelope of a finite-dimensional simple symplectic anti-Jordan triple system (AJTS). We prove that if T is a triple system as above, then there exists an ... In this work we axe concerned with the universal associative envelope of a finite-dimensional simple symplectic anti-Jordan triple system (AJTS). We prove that if T is a triple system as above, then there exists an associative algebra U(T) and an injective homomorphism ε : T→ U(T), where U(T) is an AJTS under the triple product defined by (a, b, c) = abc- cba. Moreover, U(T) is a universal object with respect to such homomorphisms. We explicitly determine the PBW-basis of U(T), the center Z(U(T)) and the Gelfand-Kirillov dimension of U(T). 展开更多
关键词 anti-Jordan triple systems universal enveloping algebras central elements PBW-bases
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Induced Modules of Restricted Lie Superalgebras 被引量:3
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作者 刘文德 《Northeastern Mathematical Journal》 CSCD 2005年第1期54-60,共7页
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i... In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules. 展开更多
关键词 restricted Lie superalgebra reduced universal enveloping algebra induced module
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DG Poisson algebra and its universal enveloping algebra 被引量:7
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作者 LU JiaFeng WANG XingTing ZHUANG GuangBin 《Science China Mathematics》 SCIE CSCD 2016年第5期849-860,共12页
We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We... We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We show that A^(ue) has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over A is isomorphic to the category of DG modules over A^(ue). Furthermore, we prove that the notion of universal enveloping algebra A^(ue) is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra. 展开更多
关键词 differential graded algebras differential graded Hopf algebras differential graded Lie algebras differential graded Poisson algebras universal enveloping algebras monoidal category
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Realizing Enveloping Algebras via Varieties of Modules 被引量:3
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作者 Ming DING Jie XIAO Fan XU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第1期29-48,共20页
By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L(A) generated by indecomposable constructible sets in the varieties of modules for any finite- dimensional C-algebra A. We ... By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L(A) generated by indecomposable constructible sets in the varieties of modules for any finite- dimensional C-algebra A. We obtain a geometric realization of the universal enveloping algebra R(A) of L(A), this generalizes the main result of Riedtmann. We also obtain Green's formula in a geometric form for any finite-dimensional C-algebra A and use it to give the comultiplication formula in R(A). 展开更多
关键词 Ringel-Hall algebra constructible set VARIETY universal enveloping algebra
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Realization of Poisson enveloping algebra 被引量:1
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作者 Can ZHU Yaxiu WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2018年第4期999-1011,共13页
For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson... For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson structure on a polynomial algebra S, we first construct a Poisson algebra R, then prove that the Poisson enveloping algebra of S is isomorphic to the specialization of the quantized universal enveloping algebra of R, and therefore, is a deformation quantization of R. 展开更多
关键词 Poisson enveloping algebra quantized universal enveloping algebra deformation quantization
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Frobenius bimodules and flat-dominant dimensions 被引量:9
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作者 Changchang Xi 《Science China Mathematics》 SCIE CSCD 2021年第1期33-44,共12页
We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslan... We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslander-Reiten conjecture on stable equivalences.We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions.Furthermore,let A and B be finite-dimensional algebras over a field k,and let domdim(_AX)stand for the dominant dimension of an A-module X.If_BM_A is a Frobenius bimodule,then domdim(A)domdim(_BM)and domdim(B)domdim(_AHom_B(M,B)).In particular,if B■A is a left-split(or right-split)Frobenius extension,then domdim(A)=domdim(B).These results are applied to calculate flat-dominant dimensions of a number of algebras:shew group algebras,stably equivalent algebras,trivial extensions and Markov extensions.We also prove that the universal(quantised)enveloping algebras of semisimple Lie algebras are QF-3 rings in the sense of Morita. 展开更多
关键词 dominant dimension extension of algebras Frobenius bimodule Frobenius part universal enveloping algebra
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Gelfand–Kirillov Dimensions of the Z^2-graded Oscillator Representations of sl(n)
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作者 Zhan Qiang BAI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第6期921-937,共17页
We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl(n,F)-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmoni... We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl(n,F)-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors 展开更多
关键词 Gelfand-Kirillov dimension highest-weight module associated variety minimal GKdimension module universal enveloping algebra
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