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Статья
2018

On Inductive Limits for Systems of C*-Algebras


R. N. GumerovR. N. Gumerov, E. V. LipachevaE. V. Lipacheva, T. A. GrigoryanT. A. Grigoryan
Русская математика
https://doi.org/10.3103/S1066369X18070083
Abstract / Full Text

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.

Author information
  • Kazan Federal University, ul. Kremlyovskaya 18, Kazan, 420008, RussiaR. N. Gumerov
  • Kazan State Power Engineering University, ul. Krasnosel’skaya 51, Kazan, 420066, RussiaE. V. Lipacheva & T. A. Grigoryan
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