Graph product Khintchine inequalities and Hecke C*-algebras
Haagerup inequalities, (non)simplicity, nuclearity and exactness
Martijn Caspers (TU Delft - Analysis)
Mario Klisse (TU Delft - Analysis)
Nadia S. Larsen (Universitetet i Oslo)
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Abstract
Graph products of groups were introduced by Green in her thesis [32]. They have an operator algebraic counterpart introduced and explored in [14]. In this paper we prove Khintchine type inequalities for general C⁎-algebraic graph products which generalize results by Ricard and Xu [50] on free products of C⁎-algebras. We apply these inequalities in the context of (right-angled) Hecke C⁎-algebras, which are deformations of the group algebra of Coxeter groups (see [22]). For these we deduce a Haagerup inequality which generalizes results from [33]. We further use this to study the simplicity and trace uniqueness of (right-angled) Hecke C⁎-algebras. Lastly we characterize exactness and nuclearity of general Hecke C⁎-algebras.
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