关于遗传代数上的例外序列自同态代数的Hochschild上同调与同调

On the Hochschild Cohomology and Homology of Endomorphism Algebras of Exceptional Sequences over Hereditary Algebras

中文关键词:  Hochschild 上同调群  例外序列  自同态代数  总体维数.

英文关键词:Hochschild cohomology groups  exceptional sequences, endomorphism algebras  global dimensions.

中文摘要:

      令$A$是代数闭域$k$上的一个有限维结合代数, $\mod A$是有限维左$A$-模范畴,$X_1,X_2,\ldots,X_n$是$\mod A$中的完全例外序列,再令$E$是$X_1,X_2,\ldots,X_n$的自同态代数,我们在本文内,研究了$E$的总体维数,计算了$E$的Hochschild上同调群和同调群.

英文摘要:

      In this paper, let $A$ be a finite dimensional associative algebra over an algebraically closed field $k$, $\mod A$ be the category of finite dimensional left $A$-module and $X_1,X_2,\ldots,X_n$ in $\mod A$ be a complete exceptional sequence, and let $E$ be the endomorphism algebra of $X_1,X_2,\ldots,X_n$. We study the global dimension of $E$, and calculate the Hochschild cohomology and homology groups of $E$.