Abstract
We study C*-algebras generated by left regular representations of right LCM one-relator monoids and Artin–Tits monoids of finite type. We obtain structural results concerning nuclearity, ideal structure and pure infiniteness. Moreover, we compute K-theory. Based on our K-theory results, we develop a new way of computing K-theory for certain group C*-algebras and crossed products.
Highlights
Ever since the work in [9,13], C*-algebras generated by isometries have provided interesting examples in the theory of general C*-algebras
C*-algebras generated by left regular representations of left-cancellative semigroups, called semigroup
C*-algebras, form a natural class of C*-algebras which have been studied for several types of semigroups
Summary
Ever since the work in [9,13], C*-algebras generated by isometries have provided interesting examples in the theory of general C*-algebras. In the non-reversible case, we show that the boundary quotient (in the sense of [18, § 5.7]) of our semigroup C*-algebra is purely infinite simple (see Corollary 3.2, where this is proven in even greater generality). Characters attached to words let us assume that our monoid P is given by a presentation ( , R) as in Sect. Since P∗ = {e} we may write P for the subset J of In this setting, let us describe ∞ by infinite words (with letters) in. Since wi contains no relator as a subword, we must have wi ≡ wj x, and w j ≡ wj
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