Module and Hochschild cohomology of certain semigroup algebras

作者：Shirinkalam A^*; Pourabbas A; Amini M

来源：Functional Analysis and Its Applications, 2015, 49(4): 315-318.

DOI：10.1007/s10688-015-0122-z

• module cohomology group
• Hochschild cohomology group
• inverse semigroup
• semigroup algebra

We study the relation between the module and Hochschild cohomology groups of Banach algebras.We show that, for every commutative Banach A-A-bimodule X and every k a N, the seminormed spaces H (A) (k) (A,X*) and H (k) (A /J,X*) are isomorphic, where J is a specific closed ideal of A. As an example, we show that, for an inverse semigroup S with the set of idempotents E, where a""(1)(E) acts on a""(1)(S) by multiplication on the right and trivially on the left, the first module cohomology (a""(1)(S), a""(1)(G (S) )((2n+1))) is trivial for each n a N, where G (S) is the maximal group homomorphic image of S. Also, the second module cohomology (a""(1)(S), a""(1)(G (S) )((2n+1))) is a Banach space.

• 出版日期2015-10