A Green--Julg isomorphism for inverse semigroups

Abstract

For every finite unital inverse semigroup $S$ and $S$-$C^{\ast }$-algebra $A$ we establish an isomorphism between $K{K}^S(\mathbb{C},A)$ and $K(A⋊S)$. This extends the classical Green--Julg isomorphism from finite groups to finite inverse semigroups.

polished version of a preprint from April 17, 2010

References in corpus (1)

• K-amenability for amalgamated free products of amenable discrete quantum groups