Symmetry and Inverse Closedness for Some Banach ∗-Algebras Associated to Discrete Groups

Abstract

A discrete group G is called rigidly symmetric if for every C*-algebra A the projective tensor product l(1)(G)(circle times) over capA is a symmetric Banach *-algebra. For such a group we show that the twisted crossed product l(alpha,omega)(1)(G; A) is also a symmetric Banach *-algebra, for every twisted action (alpha,omega omega) of G in a C*-algebra A. We extend this property to other types of decay, replacing the l(1)-condition. We also make the connection with certain classes of twisted kernels, used in a theory of integral operators involving group 2-cocycles. The algebra of these kernels is studied, both in intrinsic and in represented version.