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arXiv · 1912.09061

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. They have an operator algebraic counterpart introduced and explored by Fima and the first-named author. In this paper we prove Khintchine type inequalities for general C$^{\ast}$-algebraic graph products which generalize results by Ricard and Xu on free products of C$^{\ast}$-algebras. We apply these inequalities in the context of (right-angled) Hecke C$^{\ast}$-algebras, which are deformations of the group algebra of Coxeter groups. For these we deduce a Haagerup inequality. We further use this to study the simplicity and trace uniqueness of (right-angled) Hecke C$^{\ast}$-algebras. Lastly we characterize exactness and nuclearity of general Hecke C$^{\ast}$-algebras.

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Martijn Caspers, Mario Klisse, Nadia S. Larsen. 2019-12-19. Graph product Khintchine inequalities and Hecke C*-algebras: Haagerup inequalities, (non)simplicity, nuclearity and exactness. https://arxiv.org/abs/1912.09061

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