Journal of Operator Theory

Volume 56, Issue 1, Summer 2006 pp. 143-165.

Generalized free amalgamated product of $C^*$-algebras

Authors: Teodor S. Bildea
Author institution: Department of Mathematics, The University of Iowa 14 MacLean Hall, Iowa City, IA 52242-1419, USA

Summary: We construct a generalized version for the free product of unital $C^*$-algebras $(A_i)_{i\in I}$ with amalgamation over a family of common unital subalgebras $(B_{ij})_{i,j\in I,i\ne j}$, starting from the group-analogue. When all the algebras are the same, we recover the free product with amalgamation over a common subalgebra. We reduce the problem to the study of minimal amalgams. We specialize to triangles of algebras and subalgebras, study freeness in this context, and give some examples of constructions of minimal amalgams derived from triangles of operator algebras.

Keywords: C*-algebra, amalgam, free product, freeness with amalgamation, conditional expectation

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