scholarly journals KMS states of self-similar k-graph C*-algebras

2019 ◽  
Vol 276 (12) ◽  
pp. 3795-3831 ◽  
Author(s):  
Hui Li ◽  
Dilian Yang
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Self Similar

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 Self-similar graph $C^*$-algebras and partial crossed products

2016 ◽  
Vol 75 (2) ◽  
pp. 299-317 ◽  
Author(s):  
Ruy Exel ◽  
Starling Starling
Keyword(s):  
Crossed Products ◽  
C Algebras ◽  
Self Similar

scholarly journals Examples of non connective C *-algebras

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anna Gąsior ◽  
Andrzej Szczepański
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Blow Up ◽  
Fractional Diffusion ◽  
Uniqueness Of Solutions ◽  
C Algebras ◽  
Space Fractional Diffusion Equation ◽  
Self Similar ◽  
Similar Solutions

Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

KMS states for gauge actions on $C^*$ -algebras associated with subshifts

1998 ◽  
Vol 228 (3) ◽  
pp. 489-509 ◽  
Author(s):  
Kengo Matsumoto ◽  
Yasuo Watatani ◽  
Masamichi Yoshida
Keyword(s):  
Kms States ◽  
C Algebras

scholarly journals KMS STATES ON FINITE-GRAPH C∗-ALGEBRAS

2013 ◽  
Vol 67 (1) ◽  
pp. 83-104 ◽  
Author(s):  
Tsuyoshi KAJIWARA ◽  
Yasuo WATATANI
Keyword(s):  
Finite Graph ◽  
Kms States ◽  
C Algebras

scholarly journals KMS states on C*-algebras associated to expansive maps

2006 ◽  
Vol 134 (7) ◽  
pp. 2067-2078 ◽  
Author(s):  
Alex Kumjian ◽  
Jean Renault
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Expansive Maps

Dimension groups for self-similar maps and matrix representations of the cores of the associated C*-algebras

2020 ◽  
pp. 1-44
Author(s):  
Tsuyoshi Kajiwara ◽  
Yasuo Watatani
Keyword(s):  
Matrix Representations ◽  
Singularity Structure ◽  
Abstract Group ◽  
C Algebras ◽  
The Core ◽  
Dimension Group ◽  
Markov Shifts ◽  
Dimension Groups ◽  
Formula Group ◽  
Self Similar

Abstract We introduce a dimension group for a self-similar map as the $\mathrm {K}_0$ -group of the core of the C*-algebra associated with the self-similar map together with the canonical endomorphism. The key step for the computation is an explicit description of the core as the inductive limit using their matrix representations over the coefficient algebra, which can be described explicitly by the singularity structure of branched points. We compute that the dimension group for the tent map is isomorphic to the countably generated free abelian group ${\mathbb Z}^{\infty }\cong {\mathbb Z}[t]$ together with the unilateral shift, i.e. the multiplication map by t as an abstract group. Thus the canonical endomorphisms on the $\mathrm {K}_0$ -groups are not automorphisms in general. This is a different point compared with dimension groups for topological Markov shifts. We can count the singularity structure in the dimension groups.

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