Irregular abelian semigroups with weakly amenable semigroup algebra |
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Authors: | Hussein M. Ghlaio Charles J. Read |
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Affiliation: | 1.Department of Pure Mathematics,University of Leeds,Leeds,UK |
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Abstract: | In this paper we give counterexamples for the open problem, posed by Blackmore (Semigroup Forum 55:359–377, 1987) of whether weak amenability of a semigroup algebra ℓ 1(S) implies complete regularity of the semigroup S. We present a neat set of conditions on a commutative semigroup (involving concepts well known to those working with semigroups, e.g. the counterexamples are nil and 0-cancellative) which ensure that S is irregular (in fact, has no nontrivial regular subsemigroup), but ℓ 1(S) is weakly amenable. Examples are then given. |
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