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Vol.31 (3) 2009 — 4 results found.

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Morita equivalent subalgebras of irrational rotation algebras and real quadratic fields
C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (3) 2009, pp. 87–96
Norio Nawata (Received: 2008/10/16)

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We determine the isomorphic classes of Morita equivalent subalgebras of irrational rotation algebras. It is based on the solution of the quadratic Diophantine equations. We determine the irrational rotation algebras that have locally trivial inclusions. We compute the index of the locally trivial inclusions of irrational rotation algebras.

Nous déterminons les classes isomorphe de sous-algébres d’algébres de la rotation irrationnelle qui sont Morita-équivalente à l’algébre ambiante. Il est basé sur la solution des équations diophantienne du second degré. Nous déterminons les algébres de la rotation irrationnelle qui ont des inclusions localement triviaux. Nous calculons l’indices des inclusions localement triviaux d’algébres de la rotation irrationnelle.

AF Embedding of Crossed Products of Certain Graph ${\rm C}^*$-Algebras by Quasi-free Actions
C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (3) 2009, pp. 76–86
Xiaochun Fang (Received: 2008/10/24)

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We introduce the notion of quasi-free action of a locally compact abelian group on a graph \({\rm C}^*\)-algebra of a row-finite directed graph, with respect to a labeling of the edges of the graph by elements of the dual group, which we shall call a labeling map. A sufficient condition for AF embedding is given: if the row-finite directed graph is constructed by possibly attaching 1-loops to a row-finite directed graph each weakly connected component of which is a rooted (possibly infinite) directed tree, and the labeling map is almost proper, then the crossed product can be embedded into an AF algebra.

On introduit la notion d’action quasi-libre d’un groupe localement compact abélien sur la \({\rm C}^*\)-algèbre d’un graphe dirigé dont les rangs sont finis, par rapport à un choix d’étiquettes pour les bords du graphe par éléments du groupe dual, qu’on appellera une application d’étiquette. Une condition suffissante pour que la \({\rm C}^*\)-algèbre soit enfoncée dans une \({\rm C}\)-algèbre AF (c’est-à-dire, limite de \({\rm C}^*\)-algèbres de dimesion finie), est donnée, dans laquelle interviennent et le graphe lui-même et l’application d’étiquette.

A remark on orthogonality of elements of a C*-algebra
C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (3) 2009, pp. 72–75
George A. Elliott (Received: 2008/12/27)

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A remark on orthogonality of elements of a C*-algebra Resume/Abstract: It is shown that any two non-zero hereditary sub-C*-algebras of a C*-algebra that has no minimal projections have approximately orthogonal elements of norm one. (The question of exact orthogonality is left open.)

On démontre que, dans une C*-algèbre sans projecteur minimal, deux sous-C*-algèbres héréditaires qui ne sont pas égales à zéro possèdent des éléments de norme un qui sont approximativement orthogonals.

Polynomials à la Lehmers and Wilf
C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (3) 2009, pp. 65–71
Gert Almkvist; Arne Meurman (Received: 2009/01/23)

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We show that a period polynomial introduced by the Lehmers coincides with a generalized Wilf polynomial.

Nous montrons qu’un polynôme période introduit par les Lehmer coïncide avec un polynôme de Wilf généralisé.

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Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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