On the hochschild cohomology of finite dimensional algebras
On the hochschild cohomology of finite dimensional algebras
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DOI：
10.1080/00927878808823591
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发表时间：
1988
影响因子：
0.7
通讯作者：
Claude Cibils
中科院分区：
文献类型：
--
作者：
Claude Cibils
设k是域，Q是具有有限个顶点集Q 0和有限个箭头集Q1的连通图，kQ表示图代数。设F是由Q1生成的双边理想，设I是双边理想，其中对某个正整数h有hFcIcF 2。设A表示代数kQ/I，r表示A的根.根据Gabriel（[3]）的一个观察，所有的基本和分裂的有限维代数（即那些A/r= kx.若M是A-双模，设H*（A，M）表示M的Hochschild上同调群（见[2]）.定理：设j为大于等于2的整数。证明了对于满足tAs f0的点偶（s，t），满足下列条件：对j= Zn，t（rnnFI”-~ F）S=~（FI”+ I~ F）S，对j= 2n+1，~（FI”nI”F）~= t（~+1 +~ 1”~）S.
Let k be a field, Q be a connected quiver with finite set of vertices Q0 and finite set of arrows Q1, and let kQ denote the quiver algebra. Let F be the two sided ideal generated by Ql and let I be a two sided ideal with h F c I c F2 for some positive integer h. Let A denote the algebra kQ/I and r the radical of A. By an observation of Gabriel ([3]), all the basic and split finite dimensional algebras (ie those that A/r= kx... xk) are obtained in this way.If M is a A-bimodule, let H*(A, M) denote the Hochschild cohomology groups of M (see [2]). THEOREM: Let j a integer greater than of equal 2. Su~~ ose that for & couple of vertices(s, t) such that tAs f 0 the following conditions are satisfied: for j= Zn, t (rn n FI"-~ F) S=~(FI"+ I~ F) S for j= 2n+ l,~(FI" n I" F)~= t (~~+ l+~ 1"~) s.