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Biflatness of ℓ1-Semilattice Algebras

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Abstract

We show that if L is a semilattice then the ℓ1-convolution algebra of L is biflat precisely when L is "uniformly locally finite". Our proof technique shows in passing that if this convolution algebra is biflat then it is isomorphic as a Banach algebra to the Banach space ℓ1(L) equipped with pointwise multiplication. At the end we sketch how these techniques may be extended to prove an analogous characterisation of biflatness for Clifford semigroup algebras.

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  1. School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, England and Current address: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

    Yemon Choi

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  1. Yemon Choi
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Correspondence to Yemon Choi.

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Choi, Y. Biflatness of ℓ1-Semilattice Algebras. Semigroup Forum 75, 253–271 (2007). https://doi.org/10.1007/s00233-007-0730-x

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  • DOI: https://doi.org/10.1007/s00233-007-0730-x

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