Abstract
In this paper we characterize the Johnson pseudo-contractibility of \(\ell ^{1}(S)\), where S is a uniformly locally finite inverse semigroup. We show that for a Brandt semigroup \(S=M^{0}(G,I)\) over a non-empty set I, \(\ell ^{1}(S)\) is Johnson pseudo-contractible if and only if G is amenable and I is finite. We give some examples to show the difference between Johnson pseudo-contractibility, pseudo-amenability and pseudo-contractibility among the semigroup algebras.
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The authors are grateful to the referee for useful comments and suggestions.
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Communicated by Jan Okninski.
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Sahami, A., Pourabbas, A. Johnson pseudo-contractibility of certain semigroup algebras. Semigroup Forum 97, 203–213 (2018). https://doi.org/10.1007/s00233-017-9912-3
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DOI: https://doi.org/10.1007/s00233-017-9912-3