2021/08/22 by Astrid an Huef, Huef, Astrid an, Marcelo Laca +3
Computer Science · Mathematics · #45L05 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2108.09871
openalex publication_date 2021/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the semigroup crossed product of the additive natural numbers by\nthe multiplicative natural numbers. We study its Toeplitz C*-algebra generated\nby the right-regular representation, which we call the right Toeplitz algebra.\nWe analyse its structure by studying three distinguished quotients. We show\nthat the multiplicative boundary quotient is isomorphic to a crossed product of\nthe Toeplitz algebra of the additive rationals by an action of the\nmultiplicative rationals, and study its ideal structure. We identify the\nCrisp-Laca boundary quotient as the C*-algebra of the corresponding group built\nfrom rational numbers. There is a natural dynamics on the right Toeplitz\nalgebra and all its KMS states factor through the additive boundary quotient.\nWe describe the KMS simplex for inverse temperatures greater than one.\n