Paper's Title:

Simplicial (co)-homology of Band Semigroup

Author(s):

Yasser Farhat

Academic Support Department,
Abu Dhabi Polytechnic,
P.O. Box 111499, Abu Dhabi,
UAE.

E-mail: yasser.farhat@adpoly.ac.ae, farhat.yasser.1@gmail.com

Abstract:

We consider the Banach algebra l¹(S), with convolution, where S is a band semigroup. We prove directly, without using the cyclic cohomology, that the simplicial cohomology groups Hⁿ(l¹(S), l¹(S)^*) vanish for all n≥1. This proceeds in three steps. In each step, we introduce a bounded linear map. By iteration in each step, we achieve our goal.

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