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On module cohomology of the Fourier algebra of an inverse semigroup

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Abstract

For an inverse semigroup S with the set of idempotents E, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character amenable, module (operator) biflat and module (operator) biprojective (as \(l^1(E)\)-module). Some examples show that when S is either a bicyclic inverse semigroup or a Brandt inverse semigroup, A(S) is module amenable, module biprojective and module biflat as well.

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Acknowledgements

The authors would like to thank the reviewer for careful reading of the paper, giving some useful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran

    Abasalt Bodaghi

  2. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    Reza Rezavand

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  1. Abasalt Bodaghi
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  2. Reza Rezavand
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Correspondence to Reza Rezavand.

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Communicated by Anthony To-Ming Lau.

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Bodaghi, A., Rezavand, R. On module cohomology of the Fourier algebra of an inverse semigroup. Semigroup Forum 102, 48–61 (2021). https://doi.org/10.1007/s00233-020-10109-2

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