Amalgams of Inverse Semigroups and C*-algebras

Details Amalgams of Inverse Semigroups and C*-algebras Amalgams of Inverse Semigroups and C*-algebras

2010-07-07

arxiv.org/abs/1007.1192v1

Mathematics

Operator Algebras

Scientific paper

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], the C*-algebra of the inverse semigroup amaglam of S and T over U is the C*-algebraic amalgam of C*(S) and C*(T) over C*(U). 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.

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