Deformations of nilpotent groups and homotopy symmetric C*-algebras

Dadarlat Marius, Pennig Ulrich

Zusammenfassung

The homotopy symmetric C*-algebras are those separable C*-algebras for which one can unsuspend in E-theory. We find a new simple condition that characterizes homotopy symmetric nuclear C*-algebras and use it to show that the property of being homotopy symmetric passes to nuclear C*-subalgebras and it has a number of other significant permanence properties. As an application, we show that if I(G) is the kernel of the trivial representation i : C*(G) → ℂ for a countable discrete torsion free nilpotent group G, then I(G) is homotopy symmetric and hence the Kasparov group KK(I(G),B) can be realized as the homotopy classes of asymptotic morphisms [[I(G),B⊗K]] for any separable C*-algebra B.