The structure of C*-subalgebras of the Toeplitz algebra fixed with respect to a finite group of automorphisms

Lipacheva, E. V.; Ovsepyan, K. G.

doi:10.3103/s1066369x15060031

Cited by 11 publications

(6 citation statements)

References 7 publications

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“…We have studied earlier the C * -algebras generated by representations of ordered semigroups [7,8,9,10,11,12]. The present paper is a continuation of the study begun in the article [13].…”

Section: Introductionmentioning

confidence: 90%

Nets of graded $C^*$-algebras over partially ordered sets

Grigoryan

Lipacheva

Sitdikov

2019

St. Petersburg Math. J.

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The paper deals with C * -algebras generated by a net of Hilbert spaces over a partially ordered set. The family of those algebras constitutes a net of C * -algebras over the same set. It is shown that every such an algebra is graded by the first homotopy group of the partially ordered set. We consider inductive systems of C * -algebras and their limits over maximal directed subsets. We also study properties of morphisms for nets of Hilbert spaces as well as nets of C * -algebras.

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“…We have studied earlier the C * -algebras generated by representations of ordered semigroups [7,8,9,10,11,12]. The present paper is a continuation of the study begun in the article [13].…”

Section: Introductionmentioning

confidence: 90%

Nets of graded $C^*$-algebras over partially ordered sets

Grigoryan

Lipacheva

Sitdikov

2019

St. Petersburg Math. J.

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“…The study of such semigroup C * -algebras goes back to L. A. Coburn [13,14], R. G. Douglas [15], G. J. Murphy [16,17]. There is a large literature on the subject (see, for example, [18,19,20,21,22] and the references there in).…”

Section: Introductionmentioning

confidence: 99%

Embedding Semigroup C*-algebras into Inductive Limits

Lipacheva

2019

Lobachevskii J Math

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The note is concerned with inductive systems of Toeplitz algebras and their * -homomorphisms over arbitrary partially ordered sets. The Toeplitz algebra is the reduced semigroup C *algebra for the additive semigroup of non-negative integers. It is known that every partially ordered set can be represented as the union of the family of its maximal upward directed subsets indexed by elements of some set. In our previous work we have studied a topology on this set of indexes. For every maximal upward directed subset we consider the inductive system of Toeplitz algebras that is defined by a given inductive system over an arbitrary partially ordered set and its inductive limit. Then for a base neighbourhood U a of the topology on the set of indexes we construct the C * -algebra B a which is the direct product of those inductive limits. In this note we continue studying the connection between the properties of the topology on the set of indexes and properties of inductive limits for systems consisting of C * -algebras B a and their * -homorphisms. It is proved that there exists an embedding of the reduced semigroup C * -algebra for a semigroup in the additive group of all rational numbers into the inductive limit for the system of C * -algebras B a .

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“…Earlier the authors initiated the study of the C * -subalgebras of the Toeplitz algebra T, which is generated by the monomials with their indexes divisible by m. This C * -algebra was denoted by T m and it was proved that T m consists of the fixed points under a finite subgroup in S 1 of order m. All irreducible infinite-dimensional representations of this C * -algebra were described and complete description for all invariant ideals of the algebra T m was given (see [11][12][13]). The complete description of the group of automorphisms of C * -algebra T m and some of its subalgebras were represented in [14].…”

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confidence: 99%

“…T m as an Abstract Algebra. In this paragraph we consider the algebra T m not as a subalgebra of the classical Toeplitz algebra [11][12][13]. Here an algebra isomorphic to T m is constructed, and in the future it will be identified with T m .…”

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confidence: 99%