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Super module amenability of inverse semigroup algebras

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Abstract

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.

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Acknowledgements

The authors would like to thank the referee for careful reading. We are grateful to the office of graduate studies of the University of Isfahan for their support.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, Isfahan, Iran

    M. Lashkarizadeh Bami & M. Valaei

  2. Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-134, Iran

    M. Amini

  3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran

    M. Amini

Authors
  1. M. Lashkarizadeh Bami
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  2. M. Valaei
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  3. M. Amini
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Corresponding author

Correspondence to M. Valaei.

Additional information

Communicated by Jerome A. Goldstein.

The third author was partly supported by a grant from IPM (No. 90430215).

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Lashkarizadeh Bami, M., Valaei, M. & Amini, M. Super module amenability of inverse semigroup algebras. Semigroup Forum 86, 279–288 (2013). https://doi.org/10.1007/s00233-012-9432-0

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  • DOI: https://doi.org/10.1007/s00233-012-9432-0

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