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 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 Nonstandard Hulls of C*-Algebras and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2598
Author(s):  
Stefano Baratella
Keyword(s):  
Stochastic Processes ◽  
Convergence In Distribution ◽  
Noncommutative Probability ◽  
C Algebras ◽  
Probability Spaces ◽  
Insight Into ◽  
Hull Construction

For the sake of providing insight into the use of nonstandard techniques à la A. Robinson and into Luxemburg’s nonstandard hull construction, we first present nonstandard proofs of some known results about C*-algebras. Then we introduce extensions of the nonstandard hull construction to noncommutative probability spaces and noncommutative stochastic processes. In the framework of internal noncommutative probability spaces, we investigate properties like freeness and convergence in distribution and their preservation by the nonstandard hull construction. We obtain a nonstandard characterization of the freeness property. Eventually we provide a nonstandard characterization of the property of equivalence for a suitable class of noncommutative stochastic processes and we study the behaviour of the latter property with respect to the nonstandard hull construction.

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
Sign in / Sign up

Export Citation Format

Share Document