THE C-STAR-ALGEBRAS GENERATED BY PAIRS OF SEMIGROUPS OF ISOMETRIES SATISFYING CERTAIN COMMUTATION RELATIONS

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 = {Ut: t ∈ Γ+} and F = {St: t ∈ Λ+} satisfying the commutation relations St*Ut = e-λtI, for Λ the set of real numbers. If Λ is any subgroup of R we show that the C*-algebra UΛ generated by U and F is canonically unique. Uγ is simple if and only if Λ is dense in ℝ. © 1990 by Pacific Journal of Mathematics.