Graph product Khintchine inequalities and Hecke C*-algebras: Haagerup inequalities, (non)simplicity, nuclearity and exactness

Martijn Caspers, Mario Klisse, Nadia S. Larsen

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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.
Original languageEnglish
Article number108795
Pages (from-to)1-41
Number of pages41
JournalJournal of Functional Analysis
Volume280
Issue number1
DOIs
Publication statusPublished - 2021

Keywords

  • C -simplicity
  • Free products
  • Hecke C -algebras
  • Khintchine inequalities

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