论文标题
逆半群的紧密c*代数的新唯一定理
A new uniqueness theorem for the tight C*-algebra of an inverse semigroup
论文作者
论文摘要
我们通过概括了Brown，Nagy，Reznikoff，Sims和Williams对underemoid c*-Algebras的唯一性定理，证明了逆半群的紧密c* - 代数的紧密c*代数定理。我们用它来表明，在核和Hausdorff案例中，当右LCM单型的边界商C * - 代数中的A * - 肌形性是且仅当它在核心亚monoid产生的亚代词上的iNjective时才具有含义。我们还使用结果来阐明我们先前与子缩影相关联的逆向半群的紧密c* - 代数的身份，并错误地识别为Carlsen-Matsumoto代数。
We prove a new uniqueness theorem for the tight C*-algebras of an inverse semigroup by generalizing the uniqueness theorem given for étale groupoid C*-algebras by Brown, Nagy, Reznikoff, Sims, and Williams. We use this to show that in the nuclear and Hausdorff case, a *-homomorphism from the boundary quotient C*-algebra of a right LCM monoid is injective if and only if it is injective on the subalgebra generated by the core submonoid. We also use our result to clarify the identity of the tight C*-algebra of an inverse semigroup we previously associated to a subshift and erroneously identified as the Carlsen-Matsumoto algebra.
