КФУ. Карточка публикации. Topological Grading of Semigroup C*-Algebras

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TOPOLOGICAL GRADING OF SEMIGROUP C*-ALGEBRAS

Форма представления

Статьи в российских журналах и сборниках

Год публикации

2020

Язык

английский

Авторы, сотрудники КФУ

Гумеров Ренат Нельсонович, автор

Библиографическое описание на языке оригинала

Gumerov, R.N., Lipacheva, E.V. Topological Grading of Semigroup C*-Algebras // Herald of the Bauman Moscow State Techical University. - V. 90 - № 3, 44–54 (2020).

Аннотация

Herald of the Bauman Moscow State Techical University

Ключевые слова

grading, C*-algebra

Название журнала

Herald of the Bauman Moscow State Techical University

URL

http://vestniken.ru/eng/catalog/math/subst/925.html

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https://repository.kpfu.ru/?p_id=236809

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Гумеров Ренат Нельсонович	ru_RU
dc.date.accessioned	2020-01-01T00:00:00Z	ru_RU
dc.date.available	2020-01-01T00:00:00Z	ru_RU
dc.date.issued	2020	ru_RU
dc.identifier.citation	Gumerov, R.N., Lipacheva, E.V. Topological Grading of Semigroup C*-Algebras // Herald of the Bauman Moscow State Techical University. - V. 90 - № 3, 44–54 (2020).	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=236809	ru_RU
dc.description.abstract	Herald of the Bauman Moscow State Techical University	ru_RU
dc.description.abstract	The paper deals with the abelian cancellative semigroups and the reduced semigroup C-algebras. It is supposed that there exist epimorphisms from the semigroups onto the group of integers modulo n. For these semigroups we study the structure of the reduced semigroup C-algebras which are also called the Toeplitz algebras. Such a C-algebra can be defined for any non-abelian left cancellative semigroup. It is a very natural object in the category of C-algebras because this algebra is generated by the left regular representation of a semigroup. In the paper, by a given epimorphism σ we construct the grading of a semigroup C-algebra. To this aim the notion of the σ-index of a monomial is introduced. This notion is the main tool in the construction of the grading. We make use of the σ-index to define the linear independent closed subspaces in the semigroup C-algebra. These subspaces constitute the C-algebraic bundle, or the Fell bundle, over the group of integers modulo n. Moreover, it is shown that this grading of the reduced semigroup C-algebra is topological. As a corollary, we obtain the existence of the contractive linear operators that are non-commutative analogs of the Fourier coefficients. Using these operators, we prove the result on the geometry of the underlying Banach space of the semigroup C*-algebra	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	grading	ru_RU
dc.subject	C*-algebra	ru_RU
dc.title	Topological Grading of Semigroup C*-Algebras	ru_RU
dc.type	Статьи в российских журналах и сборниках	ru_RU