On character amenability of semigroup algebras |
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Authors: | SM Maepa |
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Institution: | Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa. E-Mail charles.maepa@up.ac.za |
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Abstract: | We study the character amenability of semigroup algebras. We work on general semigroups and certain semigroups such as inverse semigroups with a finite number of idempotents, inverse semigroups with uniformly locally finite idempotent set, Brandt and Rees semigroup and study the character amenability of the semigroup algebra l1(S) in relation to the structures of the semigroup S. In particular, we show that for any semigroup S, if ?1(S) is character amenable, then S is amenable and regular. We also show that the left character amenability of the semigroup algebra ?1(S) on a Brandt semigroup S over a group G with index set J is equivalent to the amenability of G and J being finite. Finally, we show that for a Rees semigroup S with a zero over the group G, the left character amenability of ?1(S) is equivalent to its amenability, this is in turn equivalent to G being amenable. |
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Keywords: | Primary: 46H20 Secondary: 46H10 46H25 |
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