Geodesic
On inductive limits for systems of $C^*$-algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2018), pp. 79-85

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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.
Keywords: covariant functor, direct product of $C^*$-algebras, inductive limit for an inductive system of $C^*$-algebras, partially ordered set, semigroup $C^*$-algebra, Toeplitz algebra, topology. 
@article{IVM_2018_7_a7,
     author = {R. N. Gumerov and E. V. Lipacheva and T. A. Grigoryan},
     title = {On inductive limits for systems of $C^*$-algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {79--85},
     publisher = {mathdoc},
     number = {7},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_7_a7/}
}
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R. N. Gumerov; E. V. Lipacheva; T. A. Grigoryan. On inductive limits for systems of $C^*$-algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2018), pp. 79-85. http://geodesic.mathdoc.fr/item/IVM_2018_7_a7/