Journal of Operator Theory
Volume 56, Issue 1, Summer 2006 pp. 143-165.
Generalized free amalgamated product of $C^*$-algebrasAuthors: 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.
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