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

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

2006-06-15

arxiv.org/abs/math/0606366v4

Semigroup Forum 75 (2007), no. 2, 253--271.

Mathematics

Functional Analysis

17 pages, accepted by Semigroup Forum. Some details have been added to clarify the closing remarks on the Clifford semigroup c

Scientific paper

10.1007/s00233-007-0730-x

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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