scholarly journals KMS states onC⁎-algebras associated to higher-rank graphs

2014 ◽  
Vol 266 (1) ◽  
pp. 265-283 ◽  
Author(s):  
Astrid an Huef ◽  
Marcelo Laca ◽  
Iain Raeburn ◽  
Aidan Sims
Keyword(s):  
Kms States ◽  
Higher Rank

scholarly journals Spatial realisations of KMS states on the C⁎-algebras of higher-rank graphs

2015 ◽  
Vol 427 (2) ◽  
pp. 977-1003 ◽  
Author(s):  
Astrid an Huef ◽  
Sooran Kang ◽  
Iain Raeburn
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Higher Rank

scholarly journals Cocycles on groupoids arising from -actions

2021 ◽  
pp. 1-32
Author(s):  
CARLA FARSI ◽  
LEONARD HUANG ◽  
ALEX KUMJIAN ◽  
JUDITH PACKER
Keyword(s):  
Continuous Functions ◽  
Locally Compact Abelian Group ◽  
Compact Metric Space ◽  
Kms States ◽  
Existence And Uniqueness Results ◽  
Commuting Operators ◽  
Uniqueness Results ◽  
Unit Space ◽  
Higher Rank

Abstract 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 characterization of $ 1 $ -cocycles on these groupoids taking values in a locally compact abelian group, given in terms of $ k $ -tuples of continuous functions on the unit space satisfying certain canonical identities. Using this, we develop an extended Ruelle–Perron–Frobenius theory for dynamical systems of several commuting operators ( $ k $ -Ruelle triples and commuting Ruelle operators). Results on KMS states on $ C^{\ast } $ -algebras constructed from these groupoids are derived. When the groupoids being studied come from higher-rank graphs, our results recover existence and uniqueness results for KMS states associated to the graphs.

scholarly journals Separable representations, KMS states, and wavelets for higher-rank graphs

2016 ◽  
Vol 434 (1) ◽  
pp. 241-270 ◽  
Author(s):  
Carla Farsi ◽  
Elizabeth Gillaspy ◽  
Sooran Kang ◽  
Judith A. Packer
Keyword(s):  
Kms States ◽  
Higher Rank

scholarly journals Monic representations of finite higher-rank graphs

2018 ◽  
Vol 40 (5) ◽  
pp. 1238-1267 ◽  
Author(s):  
CARLA FARSI ◽  
ELIZABETH GILLASPY ◽  
PALLE JORGENSEN ◽  
SOORAN KANG ◽  
JUDITH PACKER
Keyword(s):  
Continuous Functions ◽  
Path Space ◽  
Cyclic Vector ◽  
Kms States ◽  
Infinite Path ◽  
Representation Model ◽  
Higher Rank ◽  
Universal Representation ◽  
Comprehensive Study

In this paper, we define the notion of monic representation for the$C^{\ast }$-algebras of finite higher-rank graphs with no sources, and we undertake a comprehensive study of them. Monic representations are the representations that, when restricted to the commutative$C^{\ast }$-algebra of the continuous functions on the infinite path space, admit a cyclic vector. We link monic representations to the$\unicode[STIX]{x1D6EC}$-semibranching representations previously studied by Farsi, Gillaspy, Kang and Packer (Separable representations, KMS states, and wavelets for higher-rank graphs.J. Math. Anal. Appl. 434 (2015), 241–270) and also provide a universal representation model for non-negative monic representations.

scholarly journals KMS States on the Operator Algebras of Reducible Higher-Rank Graphs

2017 ◽  
Vol 88 (1) ◽  
pp. 91-126 ◽  
Author(s):  
Astrid an Huef ◽  
Sooran Kang ◽  
Iain Raeburn
Keyword(s):  
Operator Algebras ◽  
Kms States ◽  
Higher Rank

scholarly journals KMS states on the C⁎-algebra of a higher-rank graph and periodicity in the path space

2015 ◽  
Vol 268 (7) ◽  
pp. 1840-1875 ◽  
Author(s):  
Astrid an Huef ◽  
Marcelo Laca ◽  
Iain Raeburn ◽  
Aidan Sims
Keyword(s):  
Path Space ◽  
Kms States ◽  
C Algebra ◽  
Higher Rank

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

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