$K$-theory for the crossed products of infinite tensor product of $C^{\ast }$-algebras by the shift

Abstract

C. Schochet shows Künneth theorem for the $C^{\ast }$-algebras in the smallest class of nuclear $C^{\ast }$-algebras which contains the separable Type I algebras and is closed under some operations. We calculate the $K$-theory for the crossed product of the infinite tensor product of a unital $C^{\ast }$-algebra in this class by the shift. In particular, we calculate the $K$-theory of the lamplighter group $C^{\ast }$-algebra.

Cited by in corpus (1)

• K-homology and K-theory for the lamplighter groups of finite groups