Generalising Group Algebras

Abstract

This paper has been withdrawn by the author, since the main result, the existence and uniqueness theorem for host algebras, Theorem 3.4, is wrong for the following reasons. In Definition 3.1 we wanted to generalise the concept of an open projection away from universal enveloping Von Neumann algebras, so that it makes sense for any Von Neumann algebra N. We defined a projection P in N as open, if N.P is the intersection of left kernels of normal states of N. Unfortunately, every projection P in N will satisfy this criterion by Theorem 3.6.11 of Pedersen (C*-algebras and their automorphism groups). Hence if N = A" for a C*-algebra A, then this definition of an open projection does not define the usual open projections (cf. Proposition 3.11.9 in Pedersen). Hence the proof of Theorem 3.4, which rests on this, fails.