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Arising in the computation of the Arveson-Powers index for *endomorphisms of 93(Jo) is the notion of a pair of one-parameter semigroups of isometries %f = {Ut: t eΓ +} and S? = {St: t e Γ +} satisfying the commutation relations S*Ut = e~ λtI, for Γ the set of real numbers. If Γ is any subgroup of R we show that the C*algebra 2lp generated by % and S? is canonically unique. %lγ is simple if and only if Γ is dense in R.

TheC∗-algebras generated by pairs of semigroups of isometries satisfying certain commutation relations

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