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Biflatness of ${\ell}^1$-semilattice algebras

Yemon Choi
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Abstract

Building on an old result of Duncan and Namioka, we show that the ${\ell}^1$-convolution algebra of a semilattice $S$ is biflat precisely when $S$ is uniformly locally finite. The proof shows in passing that for such $S$ the convolution algebra is isomorphic to ${\ell}^1(S)$ 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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Yemon Choi. 2007-05-10. Biflatness of ${\ell}^1$-semilattice algebras. https://doi.org/10.1007/s00233-007-0730-x

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