scholarly journals On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II

2016 ◽  
Vol 291 ◽  
pp. 1-11 ◽  
Author(s):  
Xin Li
Keyword(s):  
Number Fields ◽  
C Algebras

scholarly journals Phase Transitions on C*-Algebras from Actions of Congruence Monoids on Rings of Algebraic Integers

2020 ◽  
Author(s):  
Chris Bruce
Keyword(s):  
Phase Transitions ◽  
Class Group ◽  
Number Fields ◽  
Algebraic Integers ◽  
Ring Of Integers ◽  
C Algebras ◽  
Rings Of Algebraic Integers ◽  
Beta 2 ◽  
Factor State ◽  
Type Classification

Abstract We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $\beta \in [1,2]$, there is a unique KMS$_\beta $ state, and we prove that it is a factor state of type III$_1$. There are phase transitions at $\beta =2$ and $\beta =\infty $ involving a quotient of a ray class group. Our computation of KMS and ground states generalizes the results of Cuntz, Deninger, and Laca for the full $ax+b$-semigroup over a ring of integers, and our type classification generalizes a result of Laca and Neshveyev in the case of the rational numbers and a result of Neshveyev in the case of arbitrary number fields.

scholarly journals $$C^*$$ -algebras of Toeplitz type associated with algebraic number fields

2012 ◽  
Vol 355 (4) ◽  
pp. 1383-1423 ◽  
Author(s):  
Joachim Cuntz ◽  
Christopher Deninger ◽  
Marcelo Laca
Keyword(s):  
Algebraic Number ◽  
Number Fields ◽  
Algebraic Number Fields ◽  
C Algebras

scholarly journals Asymptotic Semicircular Laws Induced by p-Adic Number Fields Qp and C-Algebras over Primes p*

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 819
Author(s):  
Ilwoo Cho
Keyword(s):  
Number Fields ◽  
C Algebras ◽  
Probability Spaces

In this paper, we study asymptotic semicircular laws induced both by arbitrarily fixed C * -probability spaces, and p-adic number fields { Q p } p ∈ P , as p→∞ in the set P of all primes.

scholarly journals K-THEORY FOR RING C*-ALGEBRAS: THE CASE OF NUMBER FIELDS WITH HIGHER ROOTS OF UNITY

2012 ◽  
Vol 04 (04) ◽  
pp. 449-479 ◽  
Author(s):  
XIN LI ◽  
WOLFGANG LÜCK
Keyword(s):  
Arbitrary Number ◽  
Number Fields ◽  
Roots Of Unity ◽  
C Algebras ◽  
Rings Of Integers ◽  
K Theory

We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.

An Introduction to K-Theory for C*-Algebras

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

scholarly journals Optimal transport and unitary orbits in C⁎-algebras

2021 ◽  
Vol 281 (5) ◽  
pp. 109068
Author(s):  
Bhishan Jacelon ◽  
Karen R. Strung ◽  
Alessandro Vignati
Keyword(s):  
Optimal Transport ◽  
C Algebras
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