The C^∗-algebras generated by pairs of semigroups of isometries satisfying certain commutation relations

Geoffrey Lynn Price

Vol. 146 (1990), No. 2, 315–330

DOI: 10.2140/pjm.1990.146.315

Abstract

Arising in the computation of the Arveson-Powers index for ∗-endomorphisms of B(H) is the notion of a pair of one-parameter semigroups of isometries 𝒰 = {U_t : t ∈ Γ⁺} and 𝒮 = {S_t : t ∈ Γ⁺} satisfying the commutation relations S_t^∗U_t = e^−λtI, for Γ the set of real numbers. If Γ is any subgroup of ℝ we show that the C^∗-algebra A_Γ generated by 𝒰 and 𝒮 is canonically unique. A_γ is simple if and only if Γ is dense in ℝ.

Mathematical Subject Classification 2000

Primary: 46L55

Secondary: 46L05, 47D03

Milestones

Received: 15 January 1989

Published: 1 December 1990