Date: 11 Sep 2012
Super module amenability of inverse semigroup algebras
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In this paper we compare the notions of super amenability and super module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. We find conditions for the two notions to be equivalent. In particular, we study arbitrary module actions of l 1(E S ) on l 1(S) for an inverse semigroup S with the set of idempotents E S and show that under certain conditions, l 1(S) is super module amenable if and only if S is finite. We also study the super module amenability of l 1(S)∗∗ and module biprojectivity of l 1(S), for arbitrary actions.
Communicated by Jerome A. Goldstein.
The third author was partly supported by a grant from IPM (No. 90430215).
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- Super module amenability of inverse semigroup algebras
Volume 86, Issue 2 , pp 279-288
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- Module Arense regular
- Module biprojective
- Module derivation
- Super module amenable
- Author Affiliations
- 1. Department of Mathematics, University of Isfahan, Isfahan, Iran
- 2. Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-134, Iran
- 3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran