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Hochschild(Co)homology of Galois Coverings of Grassmann Algebras

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Acta Mathematica Sinica,English Series 2009年第10期25卷 1693-1702页

作者： yun ge xu Xin TANG School of Mathematics and Computer Science Hubei University Wuhan 430062 P.R. China Department of Mathematics and Computer Science Fayetteville State University Fayetteville NC 28301 USA

Let ∧ be the Z2-Galois covering of the Grassmann algebra A over a field k of characteristic not equal to 2. In this paper, the dimensional formulae of Hochschild homology and cohomology groups of ∧ are calculated explicitly. And the cyclic homology of∧ can also be calculated when the underlying field is of characteristic zero. As a result, we prove that there is an isomorphism from i≥1 HH^i（∧） to i≥1 HH^i（∧）.

关键词： Galois covering Grassmann algebra Hochschild (co)homology minimal projective resolution

Characteristic Modules of Dual Extensions and Grobner Bases

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Acta Mathematica Sinica,English Series 2004年第6期20卷 1119-1130页

作者： yun ge xu Long Cai LI Faculty of Mathematics and Computer Science Hubei University Academy of Mathematics and Systems Science Chinese Academy of Sciences

Let C be a finite dimensional directed algebra over an algebraically closed field k and A=A(C) the dual extension of *** characteristic modules of A are constructed explicitly for a class of directed algebras,which generalizes the results of ***,it is shown that the characteristic modules of dual extensions of a certain class of directed algebras admit the left Gr(?)bner basis theory in the sense of ***.

关键词： Quasi-hereditary algebra Dual extension Characteristic module (Left)Gr(?)bner basis

Hochschild cohomology of truncated quiver algebras

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Science China Mathematics 2007年第5期50卷 727-736页

作者： yun-ge xu Yang HAN Wen-feng JIANG Faculty of Mathematics&Computer Science Hubei UniversityWuhan 430062China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080China

For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its... 详细信息

关键词： truncated quiver algebra Hochschild cohomology global dimension oriented cycle 16E40 16E10 16G10

Hochschild cohomology of special biserial algebras

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Science China Mathematics 2007年第8期50卷 1117-1128页

作者： yun-ge xu Faculty of Mathematics & Computer Science,Hubei University,Wuhan 430062,China Faculty of Mathematics & Computer Science Hubei University Wuhan 430062 China

Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.

关键词： special biserial algebra Hochschild cohomology medal 16E40 16G10

△-tame quasi-hereditary algebras

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Science China Mathematics 2007年第2期50卷 240-252页

作者： yun-ge xu & Ying-bo ZHANG Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China School of Mathematics Sciences, Beijing Normal University, Beijing 100875, China Faculty of Mathematics and Computer Science Hubei University Wuhan China School of Mathematics Sciences Beijing Normal University Beijing China

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.

关键词： bimodule problem quasi-hereditary algebra △-tameness homogeneity.