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On Inductive Limits for Systems of C*-Algebras

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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.

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Authors and Affiliations

  1. Kazan Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    R. N. Gumerov

  2. Kazan State Power Engineering University, ul. Krasnosel’skaya 51, Kazan, 420066, Russia

    E. V. Lipacheva & T. A. Grigoryan

Authors
  1. R. N. Gumerov
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  2. E. V. Lipacheva
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  3. T. A. Grigoryan
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Corresponding author

Correspondence to R. N. Gumerov.

Additional information

Original Russian Text © R.N. Gumerov, E.V. Lipacheva, T.A. Grigoryan, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 7, pp. 79–85.

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Gumerov, R.N., Lipacheva, E.V. & Grigoryan, T.A. On Inductive Limits for Systems of C*-Algebras. Russ Math. 62, 68–73 (2018). https://doi.org/10.3103/S1066369X18070083

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  • DOI: https://doi.org/10.3103/S1066369X18070083

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