Amalgams of Inverse Semigroups and C∗-Algebras

Authors

Allan P. Donsig, University of Nebraska - LincolnFollow
Steven P. Haataja
John C. Meakin, University of Nebraska - LincolnFollow

Date of this Version

2011

Citation

Indiana University Mathematics Journal c , Vol. 60, No. 4 (2011)

Comments

2000 MATHEMATICS SUBJECT CLASSIFICATION: 46L09, 20M20.

Abstract

An amalgam of inverse semigroups [S,T,U] is full if U contains all of the idempotents of S and T. We show that for a full amalgam [S,T,U], C^∗(S ∗_U T) ≅ C^∗(S) ∗_C∗(U) C^∗(T). Using this result, we describe certain amalgamated free products of C∗-algebras, including finite-dimensional C^∗-algebras, the Toeplitz algebra, and the Toeplitz C^∗-algebras of graphs.