Zobrazeno 1 - 10
of 161
pro vyhledávání: '"CLARK, LISA ORLOFF"'
Let $D \subseteq A$ be a quasi-Cartan pair of algebras. Then there exists a unique discrete groupoid twist $\Sigma \to G$ whose twisted Steinberg algebra is isomorphic to $A$ in a way that preserves $D$. In this paper, we show there is a lattice isom
Externí odkaz:
http://arxiv.org/abs/2411.15924
We prove that twisted groupoid C*-algebras are characterised, up to isomorphism, by having Cartan semigroups, a natural generalisation of normaliser semigroups of Cartan subalgebras. This extends the classic Kumjian-Renault theory to general twisted
Externí odkaz:
http://arxiv.org/abs/2407.05024
Publikováno v:
J. Math. Anal. Appl. 534 (2024), 1--13
We study the natural representation of the topological full group of an ample Hausdorff groupoid in the groupoid's complex Steinberg algebra and in its full and reduced C*-algebras. We characterise precisely when this representation is injective and
Externí odkaz:
http://arxiv.org/abs/2309.04927
We prove the equivalence of two definitions of AF groupoid in the literature: one by Renault and the other by Farsi, Kumjian, Pask and Sims. In both definitions, an AF groupoid is an increasing union of more basic groupoids, called elementary groupoi
Externí odkaz:
http://arxiv.org/abs/2309.03413
Autor:
Armstrong, Becky, Brown, Jonathan H., Clark, Lisa Orloff, Courtney, Kristin, Lin, Ying-Fen, McCormick, Kathryn, Ramagge, Jacqui
Publikováno v:
Semigroup Forum (2023), 1--15
In this note, we present criteria that are equivalent to a locally compact Hausdorff groupoid $G$ being effective. One of these conditions is that $G$ satisfies the "C*-algebraic local bisection hypothesis"; that is, that every normaliser in the redu
Externí odkaz:
http://arxiv.org/abs/2307.13814
Autor:
Clark, Lisa Orloff, Zimmerman, Joel
We construct the full and reduced C*-algebras of an ample groupoid from its complex Steinberg algebra. We also show that our construction gives the same C*-algebras as the standard constructions. In the last section, we consider an arbitrary locally
Externí odkaz:
http://arxiv.org/abs/2203.00179
Publikováno v:
J. Operator Theory 89 (2023), 285--299
We consider a locally compact Hausdorff groupoid $G$ which is graded over a discrete group. Then the fibre over the identity is an open and closed subgroupoid $G_e$. We show that both the full and reduced C*-algebras of this subgroupoid embed isometr
Externí odkaz:
http://arxiv.org/abs/2107.03650
Autor:
Armstrong, Becky, de Castro, Gilles G., Clark, Lisa Orloff, Courtney, Kristin, Lin, Ying-Fen, McCormick, Kathryn, Ramagge, Jacqui, Sims, Aidan, Steinberg, Benjamin
Publikováno v:
Int. Math. Res. Not. IMRN (2021), 1--69
We show how to recover a discrete twist over an ample Hausdorff groupoid from a pair consisting of an algebra and what we call a quasi-Cartan subalgebra. We identify precisely which twists arise in this way (namely, those that satisfy the local bisec
Externí odkaz:
http://arxiv.org/abs/2101.08556
Publikováno v:
Expositiones Mathematicae 40 (2021), 127--139
We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inv
Externí odkaz:
http://arxiv.org/abs/2010.16113
We show the reduced $C^*$-algebra of a graded ample groupoid is a strongly graded $C^*$-algebra if and only if the corresponding Steinberg algebra is a strongly graded ring. We apply this result to get a theorem about the Leavitt path algebra and $C^
Externí odkaz:
http://arxiv.org/abs/2003.04443