On Inductive Limits for Systems of <Emphasis Type="Italic">C</Emphasis>*-Algebras |
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Authors: | R N Gumerov E V Lipacheva T A Grigoryan |
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Institution: | 1.Kazan Federal University,Kazan,Russia;2.Kazan State Power Engineering University,Kazan,Russia |
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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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