On Inductive Limits for Systems of C*-Algebras View Full Text


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Article Info

DATE

2018-07

AUTHORS

R. N. Gumerov, E. V. Lipacheva, T. A. Grigoryan

ABSTRACT

We consider a covariant functor from the category of an arbitrary partially ordered set into the category of C*-algebras and their *-homomorphisms. In this case one has inductive systems of algebras over maximal directed subsets. The article deals with properties of inductive limits for those systems. In particular, for a functor whose values are Toeplitz algebras, we show that each such an inductive limit is isomorphic to a reduced semigroup C*-algebra defined by a semigroup of rationals. We endow an index set for a family of maximal directed subsets with a topology and study its properties. We establish a connection between this topology and properties of inductive limits. More... »

PAGES

68-73

References to SciGraph publications

  • 2013-03. Weierstrass polynomials and coverings of compact groups in SIBERIAN MATHEMATICAL JOURNAL
  • 2016-05. Automorphisms of some subalgebras of the Toeplitz algebra in SIBERIAN MATHEMATICAL JOURNAL
  • 2014-04. Characters and coverings of compact groups in RUSSIAN MATHEMATICS
  • 2012-06. A New Light on Nets of C*-Algebras and Their Representations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-01. C*-algebras generated by cancellative semigroups in SIBERIAN MATHEMATICAL JOURNAL
  • 2015-03. The structure of invariant ideals of some subalgebras of Toeplitz algebra in JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS (ARMENIAN ACADEMY OF SCIENCES)
  • 2015-06. The structure of C*-subalgebras of the Toeplitz algebra fixed with respect to a finite group of automorphisms in RUSSIAN MATHEMATICS
  • 2018-01. Limit Automorphisms of the C*-Algebras Generated by Isometric Representations for Semigroups of Rationals in SIBERIAN MATHEMATICAL JOURNAL
  • 2016-11. C*-algebra generated by the paths semigroup in LOBACHEVSKII JOURNAL OF MATHEMATICS
  • 1972-07. On theC*-algebra of a one-parameter semigroup of isometries in ACTA MATHEMATICA
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    http://scigraph.springernature.com/pub.10.3103/s1066369x18070083

    DOI

    http://dx.doi.org/10.3103/s1066369x18070083

    DIMENSIONS

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