A crossed product of the canonical anticommutation relations algebra in the Cuntz algebra

2014 ◽  
Vol 58 (8) ◽  
pp. 71-73 ◽  
Author(s):  
M. A. Aukhadiev ◽  
A. S. Nikitin ◽  
A. S. Sitdikov
Keyword(s):  
Crossed Product ◽  
Cuntz Algebra ◽  
Canonical Anticommutation Relations

scholarly journals The crossed product of a UHF algebra by a shift

1993 ◽  
Vol 13 (4) ◽  
pp. 615-626 ◽  
Author(s):  
Ola Bratteli ◽  
Erling Størmer ◽  
Akitaka Kishimoto ◽  
Mikael Rørdam
Keyword(s):  
Inductive Limit ◽  
Crossed Product ◽  
Cuntz Algebra ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Full Matrix ◽  
Matrix Algebras ◽  
Car Algebra ◽  
Homogeneous Algebras

AbstractWe prove that the crossed product of the CAR algebra M2∞ by the shift is an inductive limit of homogeneous algebras over the circle with fibres full matrix algebras. As a consequence the crossed product has real rank zero, and where is the Cuntz algebra of order 2.

ROHLIN FLOWS ON THE CUNTZ ALGEBRA ${\mathcal O}_2$

2002 ◽  
Vol 13 (10) ◽  
pp. 1065-1094 ◽  
Author(s):  
AKITAKA KISHIMOTO
Keyword(s):  
Crossed Product ◽  
Free Flow ◽  
Cuntz Algebra ◽  
C Algebra

We prove that a quasi-free flow on [Formula: see text] has the Rohlin property if and only if the associated crossed product is purely infinite and simple and that the quasi-free flows on [Formula: see text] with the Rohlin property are cocycle conjugate with each other. The latter result also holds for any Cuntz algebra [Formula: see text] with m < ∞. We also give some remarks on Rohlin flows on a unital separable nuclear purely infinite simple C*-algebra.

scholarly journals Simple nuclear C*-algebras not isomorphic to their opposites

2017 ◽  
Vol 114 (24) ◽  
pp. 6244-6249 ◽  
Author(s):  
Ilijas Farah ◽  
Ilan Hirshberg
Keyword(s):  
Set Theory ◽  
Inductive Limit ◽  
Axiom Of Choice ◽  
Cuntz Algebra ◽  
Car Algebra ◽  
C Algebras ◽  
Canonical Anticommutation Relations ◽  
The Axiom Of Choice

We show that it is consistent with Zermelo–Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C∗-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra.

scholarly journals The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 124
Author(s):  
Vadim Monakhov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Breaking ◽  
Momentum Space ◽  
Quantum Field ◽  
Conjugation Operator ◽  
Dirac Sea ◽  
Canonical Anticommutation Relations ◽  
The Universe ◽  
Dirac Conjugation

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

scholarly journals The Dixmier-Douady class of groupoid crossed products

2004 ◽  
Vol 76 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Paul S. Muhly ◽  
Dana P. Williams
Keyword(s):  
Crossed Product ◽  
Crossed Products ◽  
Continuous Trace

AbstractWe give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

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