Zobrazeno 1 - 10
of 386
pro vyhledávání: '"Sims, Aidan"'
We compute the nuclear dimension of extensions of C*-algebras involving commutative unital quotients and stable Kirchberg ideals. We identify the finite directed graphs whose C*-algebras are covered by this theorem.
Comment: 30 pages
Comment: 30 pages
Externí odkaz:
http://arxiv.org/abs/2409.12872
We show that the C*-algebra of a row-finite source-free k-graph is Rieffel-Morita equivalent to a crossed product of an AF algebra by the fundamental group of the k-graph. When the k-graph embeds in its fundamental groupoid, this AF algebra is a Fell
Externí odkaz:
http://arxiv.org/abs/2403.01337
We present an example of a twist over a minimal Hausdorff \'etale groupoid such that the restriction of the twist to the interior of the isotropy is not topologically trivial; that is, the restricted twist is not induced by a continuous 2-cocycle.
Externí odkaz:
http://arxiv.org/abs/2312.08683
Autor:
Mundey, Alexander, Sims, Aidan
We study the categorical homology of Zappa-Sz\'ep products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the homology of a double complex, and so can be computed via a spectral sequ
Externí odkaz:
http://arxiv.org/abs/2311.09600
Autor:
Duwenig, Anna, Sims, Aidan
We describe how to recover a Lie structure on a twist over a Hausdorff \'etale groupoid from functional-analytic data in the spirit of Connes' reconstruction theorem for manifolds. We first characterise when a smooth structure on the unit space of a
Externí odkaz:
http://arxiv.org/abs/2309.09177
We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the notion of harmonious families of bisections in etale groupoids associ
Externí odkaz:
http://arxiv.org/abs/2303.02313
Autor:
Brownlowe, Nathan, Buss, Alcides, Gonçalves, Daniel, Hume, Jeremy B., Sims, Aidan, Whittaker, Michael F.
We extend Nekrashevych's $KK$-duality for $C^*$-algebras of regular, recurrent, contracting self-similar group actions to regular, contracting self-similar groupoid actions on a graph, removing the recurrence condition entirely and generalising from
Externí odkaz:
http://arxiv.org/abs/2302.03989
We show that the Hilbert bimodule associated to a compact topological graph can be recovered from the C*-algebraic triple consisting of the Toeplitz algebra of the graph, its gauge action and the commutative subalgebra of functions on the vertex spac
Externí odkaz:
http://arxiv.org/abs/2212.09195
We prove a sandwiching lemma for inner-exact locally compact Hausdorff \'etale groupoids. Our lemma says that every ideal of the reduced $C^*$-algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined open invaria
Externí odkaz:
http://arxiv.org/abs/2211.06126
We study stable finiteness of extensions of 2-graph C*-algebras determined by saturated hereditary sets of vertices. We use two iterations of the Pimsner-Voiculescu sequence to calculate the map in K-theory induced by the inclusion of a hereditary su
Externí odkaz:
http://arxiv.org/abs/2111.15165