Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Alex Kumjian"'
Publikováno v:
Ergodic Theory and Dynamical Systems. 42:3325-3356
We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space and study generalized Ruelle operators and $ C^{\ast } $ -algebras associated to these groupoids. We provide a new characterizat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::77f70bc23ebfcc51b11f89a063fe44b5
https://doi.org/10.1017/etds.2021.69
https://doi.org/10.1017/etds.2021.69
We analyse extensions $\Sigma$ of groupoids $G$ by bundles $A$ of abelian groups. We describe a pushout construction for such extensions, and use it to describe the extension group of a given groupoid $G$ by a given bundle $A$. There is a natural act
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94f04bdc5706ed29e4a216f8bdbbd3c0
Publikováno v:
Journal of Functional Analysis
Journal of Functional Analysis, Elsevier, In press, 280 (5), pp.108892. ⟨10.1016/j.jfa.2020.108892⟩
Journal of Functional Analysis, Elsevier, In press, 280 (5), pp.108892. ⟨10.1016/j.jfa.2020.108892⟩
Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algebras determined by $\mathcal A$ whose twisted crossed
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1503b257406df4603b1a4a84664e3f0a
http://arxiv.org/abs/2001.01312
http://arxiv.org/abs/2001.01312
Autor:
Elizabeth Gillaspy, Alex Kumjian
Publikováno v:
Banach J. Math. Anal. 12, no. 3 (2018), 572-599
Given a higher-rank graph $\Lambda$, we investigate the relationship between the cohomology of $\Lambda$ and the cohomology of the associated groupoid $G_\Lambda$. We define an exact functor between the abelian category of right modules over a higher
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e44aafec349a3e096340b0b38c4a8dc
https://doi.org/10.1215/17358787-2017-0041
https://doi.org/10.1215/17358787-2017-0041
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 148:79-100
We study the $C^*$-algebras associated to upper-semicontinuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer--Raeburn "Stabilization Trick," we construct from each such bundle a groupoid dynamical sys
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f2419394787944af4f61dd09f5fe5f07
https://doi.org/10.1017/s0308210517000129
https://doi.org/10.1017/s0308210517000129
Autor:
Hui Li, Alex Kumjian
Publikováno v:
Journal of Operator Theory. 78:201-225
The second author showed how Katsura's construction of the C*-algebra of a topological graph E may be twisted by a Hermitian line bundle L over the edge space E. The correspondence defining the algebra is obtained as the completion of the compactly s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3233decfee91d740374dc6ec9bea78ce
https://doi.org/10.7900/jot.2016jun23.2136
https://doi.org/10.7900/jot.2016jun23.2136
Given a locally compact abelian group G, we give an explicit formula for the Dixmier-Douady invariant of the C∗-algebra of the groupoid extension associated to a Cech 2-cocycle in the sheaf of germs of continuous G-valued functions. We then exploit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1998e14afc12d2338380a59ee529d12e
Publikováno v:
Transactions of the American Mathematical Society. 367:5177-5216
We define the categorical cohomology of a k k -graph Λ \Lambda and show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This leads to an alternative characteris
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::05f144a28165c3046fa99f1079c2b545
https://doi.org/10.1090/s0002-9947-2015-06209-6
https://doi.org/10.1090/s0002-9947-2015-06209-6
Publikováno v:
Journal of Mathematical Analysis and Applications. 401:104-113
We investigate the K -theory of twisted higher-rank-graph algebras by adapting parts of Elliott’s computation of the K -theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::522c2175c4153ca9c88258ad064546c2
https://doi.org/10.1016/j.jmaa.2012.11.030
https://doi.org/10.1016/j.jmaa.2012.11.030
Autor:
David Pask, Alex Kumjian
Publikováno v:
Ergodic Theory and Dynamical Systems. 23:1153-1172
An action of Zk is associated to a higher rank graph Λ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We show that the stable Ruelle algebra of Λ is strongly
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::131c51c76f02e4abe03daf46f612b150
https://doi.org/10.1017/s0143385702001670
https://doi.org/10.1017/s0143385702001670