共查询到20条相似文献,搜索用时 15 毫秒
1.
Tubular algebras and affine Kac-Moody algebras 总被引:1,自引:0,他引:1
Zheng-xin CHEN & Ya-nan LIN School of Mathematics Computer Science Pujian Normal University Fuzhou China School of Mathematical Sciences Xiamen University Xiamen China 《中国科学A辑(英文版)》2007,50(4):521-532
The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules. 相似文献
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Piecewise-Koszul algebras 总被引:4,自引:0,他引:4
Jia-feng L~ Ji-wei HE~ Di-ming LU~ 《中国科学A辑(英文版)》2007,50(12):1795-1804
It is a small step toward the Koszul-type algebras.The piecewise-Koszul algebras are, in general,a new class of quadratic algebras but not the classical Koszul ones,simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases.We give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A),and show an A_∞-structure on E(A).Relations between Koszul algebras and piecewise-Koszul algebras are discussed.In particular,our results are related to the third question of Green-Marcos. 相似文献
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Let A be an Artin algebra. If $V\in \operatorname{mod} A$ such that the global dimension of $\operatorname{End}_{A}V$ is at most 3, then for any ${M\in \operatorname{add}_{A}V}$ , both B and B op are 2-Igusa–Todorov algebras, where ${B=\operatorname{End}_{A}M}$ . Let ${P\in \operatorname{mod} A}$ be projective and ${B=\operatorname{End}_{A}P}$ such that the projective dimension of P as a right B-module is at most n(<∞). If A is an m-syzygy-finite algebra (resp. an m-Igusa–Todorov algebra), then B is an (m+n)-syzygy-finite algebra (resp. an (m+n)-Igusa–Todorov algebra); in particular, the finitistic dimension of B is finite in both cases. Some applications of these results are given. 相似文献
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Xiao-yuan Chen 《高校应用数学学报(英文版)》2008,23(3):366-370
Results of the research for smash product algebras over dimodule algebras are generalized to the more general twisted dimodule algebras. 相似文献
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Xinhong Chen 《代数通讯》2017,45(2):849-865
For any skewed-gentle algebra, we characterize its indecomposable Gorenstein projective modules explicitly and describe its Cohen–Macaulay Auslander algebra. We prove that skewed-gentle algebras are always Gorenstein, which is independent of the characteristic of the ground field, and the Cohen–Macaulay Auslander algebras of skewed-gentle algebras are also skewed-gentle algebras. 相似文献
6.
Martin Schlichenmaier 《代数通讯》2017,45(2):776-821
We show how the recently again discussed N-point Witt, Virasoro, and a?ne Lie algebras are genus zero examples of the multipoint versions of Krichever–Novikov-type algebras as introduced and studied by Schlichenmaier. Using this more general point of view, useful structural insights and an easier access to calculations can be obtained. The concept of almost-grading will yield information about triangular decompositions which are of importance in the theory of representations. As examples, the algebra of functions, vector fields, differential operators, current algebras, a?ne Lie algebras, Lie superalgebras, and their central extensions are studied. Very detailed calculations for the three-point case are given. 相似文献
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We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda
algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki’s categorification
theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial ℤ-grading on blocks of
cyclotomic Hecke algebras, including symmetric groups in positive characteristic. 相似文献
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ZHU Linsheng Department of Mathematics Changshu Institute of Technology Changshu China 《中国科学A辑(英文版)》2006,49(4):477-493
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way. 相似文献
12.
Central simple Poisson algebras 总被引:1,自引:0,他引:1
SU Yucai & XU XiaopingDepartment of Mathematics Shanghai Jiaotong University Shanghai China Institute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2004,47(2):245-263
Poisson algebras are fundamental algebraic structures in physics and sym-plectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero. The Lie algebra structures of these Poisson algebras are in general not finitely-graded. 相似文献
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Yun-ge XU & Ying-bo ZHANG Faculty of Mathematics Computer Science Hubei University Wuhan China School of Mathematics Sciences Beijing Normal University Beijing China 《中国科学A辑(英文版)》2007,50(2):240-252
Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous. 相似文献
14.
Fang Jie 《中国科学A辑(英文版)》2008,51(2):185-194
In this paper,we study a certain class of double Ockham algebras (L;∧,∨,f,k,0,1), namely the bounded distributive lattices (L;∧,∨,0,1) endowed with a commuting pair of unary op- erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both (L;f) and (L;k) are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple. 相似文献
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S. A. Grigorian M. I. Karakhanyan T. A. Khor’kova 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(6):313-319
The paper studies the properties of β-uniform Dirichlet algebras and maximal β-uniform algebras. A method is given for construction of a β-uniform Dirichlet algebra and a maximal β-uniform algebra by means of a uniform Dirichlet algebra and amaximal uniform algebra respectively. As a consequence, an analog of the Bishop-Shilov theorem on antisymmetric partition is obtained. 相似文献
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A. Walendziak 《Periodica Mathematica Hungarica》1991,23(3):219-226
In the present paper we give a common generalization of subdirect product, direct product and weak direct product of given algebras.
Mathematics subject classification numbers, 1980/85 Primary 08A30; Secondary 061310. 相似文献