The Glimm space of the minimal tensor product of C*-algebras
Dave McConnell (Trinity College Dublin)
Tuesday 22nd January, 2013 16:00-17:00 Maths 203
We consider a C*-algebra A and its space of Primitive ideals Prim(A) in its usual hull-kernel topology. The Glimm space of A, Glimm(A), is defined as the complete regularisation of Prim(A) - the quotient of Prim(A) modulo the relation of inseparability by continuous functions, with topology induced by the continuous functions on Prim(A). To each such equivalence class in Prim(A) we assign a (closed, two-sided) ideal of A given by the intersection of the primitive ideals contained in it. Thus Glimm(A) may be regarded as a set of ideals of A. For the minimal tensor product A \otimes B of C*-algebras A and B we describe Glimm (A \otimes B ) in terms of Glimm(A) and Glimm(B), both topologically and as a set of ideals of A \otimes B, generalising a result of Kaniuth (1994). We apply this to the study of the centre of the multiplier algebra of A \otimes B.