Book•
C-Algebras and Their Automorphism Groups
01 Jun 1979-
About: The article was published on 1979-06-01 and is currently open access. It has received 2826 citations till now. The article focuses on the topics: Inner automorphism & Outer automorphism group.
Citations
More filters
TL;DR: In this article, uncertainty relations for the different coordinates of spacetime events are proposed, motivated by Heisenberg's principle and by Einstein's theory of classical gravity, and a model of Quantum Spacetime is discussed where the commutation relations exactly implement our uncertainty relations.
Abstract: We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations.
1,453 citations
TL;DR: In this paper, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of publication mathématique de l'I.H.É.S.
Abstract: © Publications mathématiques de l’I.H.É.S., 1985, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
1,149 citations
TL;DR: In this paper, the authors present a class of C*-algebras and point out its close relationship to topological Markov chains, whose theory is part of symbolic dynamics.
Abstract: In this paper we present a class of C*-algebras and point out its close relationship to topological Markov chains, whose theory is part of symbolic dynamics. The C*-algebra construction starts from a matrix A =(A (i,j))i,~ z, Z a finite set, A(i,j)c{0, l}, and where every row and every column of A is non-zero. (That A(i,j)e{O, 1} is assumed for convenience only. All constructions and results extend to matrices with entries in 2~+. We comment on this in Remark 2.18.) A C*-algebra 6~ A is then generated by partial isometries Si~O(i~X ) that act on a Hilbert space in such a way that their support projections Qi=S*S~ and their range projections P~ =SIS* satisfy the relations
1,042 citations
Cites background from "C-Algebras and Their Automorphism G..."
...[14]) sd of J by the automorphism group that is induced by (r on ~....
[...]
1,025 citations
TL;DR: In this paper, it was shown that the transformation group C*-algebra for the action of the integers on the circle by powers of the rotation by angle 2πa is not isomorphic for different irrational numbers, except for some obvious redundancies.
Abstract: For any irrational number a let Aa be the transformation group C*-algebra for the action of the integers on the circle by powers of the rotation by angle 2πa. It is known that Aa is simple and has a unique normalized trace, τ. We show that for every β in (Z + Za) Π [0,1] there is a projection p in Aa with τ(p) = β. When this fact is combined with the very recent result of Pimsner and Voiculescu that if p is any projection in Aa then τ{p) must be in the above set, one can immediately show that, except for some obvious redundancies, the Aa are not isomorphic for different a. Moreover, we show that Aa and Aβ are strongly Morita equivalent exactly if a and β are in the same orbit under the action of GL (2, Z) on irrational numbers. 0* Introduction* Let a be an irrational number, and let S
723 citations