Date of this Version
Indiana University Mathematics Journal c , Vol. 60, No. 4 (2011)
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.