The ideal structure of C∗-algebras related to lattice-ordered groups.

Suppose that (G , G +) is a lattice-ordered abelian group with positive cone G + . Adji and Raeburn have shown a result about the structure of the primitive ideal space of the C ∗ -algebra B G + × α G + for a totally ordered abelian group (Adji and Raeburn in Integral Equ Oper Theory 48:281–293, 2004, Theorem 3.1). In this paper, we show if ∑ (G) is the chain of subgroups H of G, where H : = H + - H + and H + is any hereditary subsemigroup of G + . Then, there exists a well-defined map F from the disjoint union ⨆ { H ^ : H ∈ ∑ G } to the primitive ideals of the C ∗ -algebra B G + × α G + . Our result is interesting and has more challenges, since we are working under the assumption that the group G is lattice-ordered and extends their result to more general cases. [ABSTRACT FROM AUTHOR]