Amalgams of Inverse Semigroups and C*-algebras

2010/07/07 by Allan P Donsig, Donsig, Allan P, Steven P. Haataja +3
Mathematics · #20M20 #46L09 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:20M20 #msc:46L09

paper · pdf · doi:10.48550/arxiv.1007.1192

arxiv created 2010/07/07 · arxiv updated 2010/07/08

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], 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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