


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.
Email: yasser.farhat@adpoly.ac.ae, farhat.yasser.1@gmail.com
Abstract:
We consider the Banach algebra l^{1}(S), with convolution, where S is a band semigroup. We prove directly, without using the cyclic cohomology, that the simplicial cohomology groups H^{n}(l^{1}(S), l^{1}(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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