GROUND STATES OF A COVARIANT SEMIGROUP C∗-ALGEBRA

Abstract

Let P (cid:111) N× be a semidirect product of an additive semigroup P = {0, 2, 3, · · · } by a multiplicative positive natural numbers semigroup N×. We consider a covariant semigroup C ∗algebra T (P(cid:111)N×) of the semigroup P(cid:111)N×. We obtain the condition that a state on T (P (cid:111) N×) can be a ground state of the natural C ∗dynamical system (T (P (cid:111) N×), R, σ).

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