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Simplicity of right-angled Hecke \(C^*\)-algebras. (English) Zbl 1521.46024

Summary: By exploiting properties of boundaries associated with Coxeter groups we obtain a complete characterization of simple right-angled multi-parameter Hecke \(C^{\ast}\)-algebras. This extends previous results by Caspers, Larsen, and the author [M. Caspers et al., J. Funct. Anal. 280, No. 1, Article ID 108795, 41 p. (2021; Zbl 1451.05199)]. Based on a work by S. Raum and A. Skalski [J. Math. Pures Appl. (9) 172, 265–298 (2023; Zbl 1519.46049)], we further describe the center and the character space of right-angled Hecke \(C^{\ast}\)-algebras.

MSC:

46L35 Classifications of \(C^*\)-algebras
46L06 Tensor products of \(C^*\)-algebras
20C08 Hecke algebras and their representations