GROUND STATES OF A COVARIANT SEMIGROUP C-ALGEBRA

• Published in: 충청수학회지, 33(3) pp. 339 - 349
• Main Authors: 장선영, 안지은
• Format: Journal Article
• Language: English
• Published: 충청수학회 01.08.2020
• Subjects: 수학
• ISSN: 1226-3524; 2383-6245
• DOI: 10.14403/jcms.2020.33.3.339

Let $ \mathrm{P}\rtimes\Bbb N^{\times}$ be a semidirect product of an additive semigroup$ \mathrm{P} = \{ 0, 2, 3, \cdots \} $by a multiplicative positive natural numbers semigroup $ \Bbb N^{\times}$. We consider a covariant semigroup $C^{*}$-algebra $ {\mathcal{T}}(\mathrm{P} \rtimes \mathbb{N}^{\times})$ of the semigroup $ \mathrm{P}\rtimes\Bbb N^{\times}$. We obtain the condition that a state on $ {\mathcal{T}}(\mathrm{P} \rtimes \mathbb{N}^{\times})$ can be a ground state ofthe natural $C^*$-dynamical system $( \mathcal{T} ( \mathrm{P}\rtimes\Bbb N^{\times}), \Bbb R, \sigma )$. KCI Citation Count: 0