KMS states of a generalized Toeplitz algebras

Abstract

In this paper, we consider a generalized Toeplitz algebra $\mathcal{T}(\mathrm{P}⋊{\mathbb{N}}^{\times })$ for a non-quasi-lattice ordered semigroup $\mathrm{P}⋊{\mathbb{N}}^{\times }$ where $\mathrm{P}⋊{\mathbb{N}}^{\times }$ is a semidirect product of an additive semigroup $\mathrm{P}=\{0,2,3,\cdots \}$ by a multiplicative positive natural numbers semigroup ${\mathbb{N}}^{\times }$. And also we compute the values of the KMS state of the natural $C^{\ast }$-dynamical system $(\mathcal{T}(\mathrm{P}⋊{\mathbb{N}}^{\times }),\mathbb{R},\sigma ).$

17 pages

References in corpus (1)

• The Regular C*-algebra of an Integral Domain