In this paper,it is proved that, let M be a tubular module, then there is a tubular module N,such that End(MN) is a quasi-hereditary algebra. And in the case of M bing a indeconposable tubular module, th...In this paper,it is proved that, let M be a tubular module, then there is a tubular module N,such that End(MN) is a quasi-hereditary algebra. And in the case of M bing a indeconposable tubular module, this paper characterizes the below bound of the number of indecomposable direct summands of N.展开更多
已知自由代数 Fm 的 E（n）-模代数 Fm（Γ），对于数域 k 上的任一 m × m 矩阵 A，笔者定义了 Fm（Γ）的一个代数自同态φA ，证明了φA 是 Fm（Γ）的一个 E（n）-模代数自同构的充要条件是ΓA =Γ，并进一步给出了φA 成为两...已知自由代数 Fm 的 E（n）-模代数 Fm（Γ），对于数域 k 上的任一 m × m 矩阵 A，笔者定义了 Fm（Γ）的一个代数自同态φA ，证明了φA 是 Fm（Γ）的一个 E（n）-模代数自同构的充要条件是ΓA =Γ，并进一步给出了φA 成为两个不同的 E（n）-模代数之间同构的等价条件。展开更多
Some properties about stable subset S(θ n) and image Im(θ n) of self homomorphism \{θ n:x→0*x n\} are discussed. The characterization that Im(θ n) becomes an ideal of BCI algebra X is given.
Let An be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra Endox （T） of a tilting complex T = II^ni=0^Ox （i） of coherent COx-modul...Let An be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra Endox （T） of a tilting complex T = II^ni=0^Ox （i） of coherent COx-modules over a projective scheme X = P^nk. In this paper we first construct a minimal projective bimodule resolution of An, and then apply it to calculate k-dimensions of the Hochsehild cohomology groups of An in terms of parallel paths. Finally, we give an explicit description of the cup product and obtain a Gabriel presentation of Hochschild cohomology ring of An. As a consequence, we provide a class of algebras of finite global dimension whose Hochschild cohomology rings have non-trivial multiplicative structures.展开更多
In this paper, let A be a finite dimensional associative algebra over an algebraically closed field h, modA be the category of finite dimensional left A-module and X1,X2,... ,X2, in modA be a complete exceptional sequ...In this paper, let A be a finite dimensional associative algebra over an algebraically closed field h, modA be the category of finite dimensional left A-module and X1,X2,... ,X2, in modA be a complete exceptional sequence, and let E be the endomorphism algebra of X1, X2,..., Xn. We study the global dimension of E, and calculate the Hochschild cohomology and homology groups of E.展开更多
文摘In this paper,it is proved that, let M be a tubular module, then there is a tubular module N,such that End(MN) is a quasi-hereditary algebra. And in the case of M bing a indeconposable tubular module, this paper characterizes the below bound of the number of indecomposable direct summands of N.
文摘已知自由代数 Fm 的 E（n）-模代数 Fm（Γ），对于数域 k 上的任一 m × m 矩阵 A，笔者定义了 Fm（Γ）的一个代数自同态φA ，证明了φA 是 Fm（Γ）的一个 E（n）-模代数自同构的充要条件是ΓA =Γ，并进一步给出了φA 成为两个不同的 E（n）-模代数之间同构的等价条件。
文摘Some properties about stable subset S(θ n) and image Im(θ n) of self homomorphism \{θ n:x→0*x n\} are discussed. The characterization that Im(θ n) becomes an ideal of BCI algebra X is given.
基金supported by National Natural Science Foundation of China (Grant Nos.10971206 and 11171325)Important Foundation of Hubei Provincial Department of Education (Grant No.D20101003)
文摘Let An be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra Endox （T） of a tilting complex T = II^ni=0^Ox （i） of coherent COx-modules over a projective scheme X = P^nk. In this paper we first construct a minimal projective bimodule resolution of An, and then apply it to calculate k-dimensions of the Hochsehild cohomology groups of An in terms of parallel paths. Finally, we give an explicit description of the cup product and obtain a Gabriel presentation of Hochschild cohomology ring of An. As a consequence, we provide a class of algebras of finite global dimension whose Hochschild cohomology rings have non-trivial multiplicative structures.
基金the Research Group "Classification of Algebraic Surfaces and Compact Complex Manifolds" of the Deutsche Forschungsgemeinschaft DFG for financial support
文摘We classify non-algebraic compact Khler threefolds admitting an endomorphism f:X → X of degree at least two.
基金the National Natural Science Foundation of China （No. 10371036 10671061）+2 种基金 the Natural Science Foundation of Beijing （1042001） the Fund of Beijing Education Committee （No. KM200610005024） Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality and the Fundamental reseaxch Fund of Beijing University of Technology.
文摘In this paper, let A be a finite dimensional associative algebra over an algebraically closed field h, modA be the category of finite dimensional left A-module and X1,X2,... ,X2, in modA be a complete exceptional sequence, and let E be the endomorphism algebra of X1, X2,..., Xn. We study the global dimension of E, and calculate the Hochschild cohomology and homology groups of E.
