Operator Algebra Seminar

Abstract: In recent years, graph products of operator algebras have attracted growing interest, particularly in relation to free probability, Popa’s deformation/rigidity theory, and approximation properties. Furthermore, von Neumann algebras arising from group-theoretic graph products have been studied intensively. In contrast, comparatively little is known about their C*-algebraic counterparts beyond the free product case.

In this talk, I present a framework for analyzing structural properties of graph product C-algebras by introducing a natural class of C-algebras generated by reduced graph products and families of projections associated with words in right-angled Coxeter groups. These algebras possess a rich and tractable combinatorial structure, which enables the deduction of a variety of properties. Among other things, I will discuss universal properties, approximation properties, and analyze the ideal structure. I will then explain how to leverage this framework to derive new insights into the structure of graph product C*-algebras – many of which are novel even in the case of free products.