We study C*-algebras generated by representations of product systems over unital subsemigroups of amenable discrete groups. In the first part, we show that exactness of the generated C*-algebra is equivalent to exactness of the cores over the constructible ideals. Nuclearity of the generated C*-algebra is equivalent to nuclear embeddability of the cores in the fixed point algebra. In the second part, we further study injective equivariant Fock covariant representations, and whether the properties of the cores are inherited from properties of the coefficient C*-algebra, as in the case of compactly aligned saturated product systems over right LCM semigroups. If the semigroup is finitely aligned and the product system is saturated and compactly aligned, then exactness of the cores is equivalent to exactness of the coefficient C*-algebra. If in addition the semigroup is strongly finitely aligned, then nuclear embeddability of the cores is equivalent to nuclear embeddability of the coefficient C*-algebra. These results do not hold without the compact alignment hypothesis, even for right LCM semigroups.
We prove Z-stability for all simple, separable, pure, nuclear C*-algebras. Combining this with very recent work of Thiel completes the proof of the Toms-Winter conjecture. We do this through the framework of II_1 factorial tracially complete C*-algebras. We characterise regularity for these algebras in various terms. I...
Samuel Evington, Shan-Shan Hua, Christopher Schafhauser et al.· 1 citation· ⚡1
We characterize the von Neumann algebras that are isomorphic, as $C^*$-algebras, to reduced twisted $C^*$-algebras of locally compact Hausdorff groupoids equipped with continuous Haar systems of full support. They are exactly the subhomogeneous von Neumann algebras, equivalently finite products of matrix algebras over...
Alcides Buss, Luiz Felipe Garcia, T. Pacheco· 1 citation
We study locally finite-dimensional ideals in crossed products of totally disconnected spaces by free actions of the integers and in uniform Roe algebras of exact discrete groups. In the first case, we present a dynamical description of the largest locally finite-dimensional ideal, which turns out to coincide with the...
In this paper, we investigate the structure of a twisted C*‐algebra , built on a unital C*‐algebra using a central projection and a unitary . The operations are defined as and . A key insight we uncover is that this twisted setup is ‐isomorphic to the direct sum . Building on that isomorphism, we offer detailed descr...
Ercan Çelik, Ali Jabbari· Mathematische Nachrichten· 0 citations
We propose to define amenability of a Lie algebra by the existence of almost-invariant finite-dimensional subcoalgebras of its universal enveloping algebra. More generally, a module coalgebra of a cocommutative Hopf algebra is amenable if it admits almost-invariant finite-dimensional subcoalgebras. We prove a coalgebra...
L. Bartholdi· 0 citations
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