scholarly journals Cartan subalgebras in C*-algebras. Existence and uniqueness

2019 ◽  
Vol 372 (3) ◽  
pp. 1985-2010 ◽  
Author(s):  
Xin Li ◽  
Jean Renault
Keyword(s):  
Existence And Uniqueness ◽  
C Algebras ◽  
Cartan Subalgebras

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.

scholarly journals MORPHISMS OF SIMPLE TRACIALLY AF ALGEBRAS

2004 ◽  
Vol 15 (09) ◽  
pp. 919-957 ◽  
Author(s):  
MARIUS DADARLAT
Keyword(s):  
Existence And Uniqueness ◽  
Residually Finite ◽  
C Algebras ◽  
Finite Dimensional ◽  
K Theory ◽  
Inner Automorphisms ◽  
Af Algebras ◽  
Universal Coefficient Theorem

Let A, B be separable simple unital tracially AF C*-algebras. Assuming that A is exact and satisfies the Universal Coefficient Theorem (UCT) in KK-theory, we prove the existence, and uniqueness modulo approximately inner automorphisms, of nuclear *-homomorphisms from A to B with prescribed K-theory data. This implies the AF-embeddability of separable exact residually finite-dimensional C*-algebras satisfying the UCT and reproves Huaxin Lin's theorem on the classification of nuclear tracially AF C*-algebras.

scholarly journals Cartan subalgebras for non-principal twisted groupoid C⁎-algebras

2020 ◽  
Vol 279 (6) ◽  
pp. 108611 ◽  
Author(s):  
A. Duwenig ◽  
E. Gillaspy ◽  
R. Norton ◽  
S. Reznikoff ◽  
S. Wright
Keyword(s):  
C Algebras ◽  
Cartan Subalgebras

scholarly journals Cartan subalgebras and the UCT problem, II

2020 ◽  
Vol 378 (1-2) ◽  
pp. 255-287
Author(s):  
Selçuk Barlak ◽  
Xin Li
Keyword(s):  
Algebraic Topology ◽  
Classification Theory ◽  
Cuntz Algebra ◽  
Crossed Products ◽  
C Algebra ◽  
C Algebras ◽  
Cyclic Groups ◽  
Open Questions ◽  
Cartan Subalgebras ◽  
Stably Finite

Abstract We study the connection between the UCT problem and Cartan subalgebras in C*-algebras. The UCT problem asks whether every separable nuclear C*-algebra satisfies the UCT, i.e., a noncommutative analogue of the classical universal coefficient theorem from algebraic topology. This UCT problem is one of the remaining major open questions in the structure and classification theory of simple nuclear C*-algebras. Since the class of separable nuclear C*-algebras is closed under crossed products by finite groups, it is a natural and important task to understand the behaviour of the UCT under such crossed products. We make a contribution towards a better understanding by showing that for certain approximately inner actions of finite cyclic groups on UCT Kirchberg algebras, the crossed products satisfy the UCT if and only if we can find Cartan subalgebras which are invariant under the actions of our finite cyclic groups. We also show that the class of actions we are able to treat is big enough to characterize the UCT problem, in the sense that every such action (even on a particular Kirchberg algebra, namely the Cuntz algebra $$\mathcal O_2$$ O 2 ) leads to a crossed product satisfying the UCT if and only if every separable nuclear C*-algebra satisfies the UCT. Our results rely on a new construction of Cartan subalgebras in certain inductive limit C*-algebras. This new tool turns out to be of independent interest. For instance, among other things, the second author has used it to construct Cartan subalgebras in all classifiable unital stably finite C*-algebras.

scholarly journals Cartan Subalgebras in C*-Algebras of Haus dorff étale Groupoids

2016 ◽  
Vol 85 (1) ◽  
pp. 109-126 ◽  
Author(s):  
Jonathan H. Brown ◽  
Gabriel Nagy ◽  
Sarah Reznikoff ◽  
Aidan Sims ◽  
Dana P. Williams
Keyword(s):  
C Algebras ◽  
Cartan Subalgebras

scholarly journals Classification of Certain Simple C*-Algebras with Torsion in K1

2001 ◽  
Vol 53 (6) ◽  
pp. 1223-1308 ◽  
Author(s):  
Jesper Mygind
Keyword(s):  
Existence And Uniqueness ◽  
Building Blocks ◽  
Uniqueness Theorems ◽  
Inductive Limits ◽  
Direct Sums ◽  
Existence And Uniqueness Theorems ◽  
Infinite Dimensional ◽  
C Algebras ◽  
Image Position

AbstractWe show that the Elliott invariant is a classifying invariant for the class of ${{C}^{*}}$-algebras that are simple unital infinite dimensional inductive limits of finite direct sums of building blocks of the form$$\left\{ f\in C\left( \mathbb{T} \right)\otimes {{M}_{n}}:f\left( {{x}_{i}} \right)\in {{M}_{{{d}_{i}}}},i=1,2,...,N \right\},$$where ${{x}_{1}},\,{{x}_{2.}},...,{{x}_{N\,}}\in \mathbb{T},{{d}_{1}},{{d}_{2}},.\,.\,.,{{d}_{N}}$ are integers dividing $n$, and ${{M}_{{{d}_{i}}}}$ is embedded unitally into ${{M}_{n}}$. Furthermore we prove existence and uniqueness theorems for $*$-homomorphisms between such algebras and we identify the range of the invariant.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory
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