ThesisAuthors: Haataja, Steven P. (2006)
We focus on three constructions: amalgamated free products of inverse semi-groups, C*-algebras of inverse semigroups, and amalgamated free products of C*-algebras. The starting point is an amalgam [S1, S2, U] of inverse semigroups that is full, i.e., the embeddings of U into S1 and S2 are bijective on the semilattice of idempotents. Although the order structure of the amalgamated free product is well-understood, the structure of the maximal subgroups was somewhat mysterious prior to this work. We use Bass-Serre theory to characterize these maximal subgroups and determine which graphs of groups arise in this setting. We obtain necessary and sufficient conditions for the amalgamated free product to have trivial subgroups. One surprising consequence is that an amalgamated free product ...