KFU. Card publication. Topological Grading of Semigroup C*-Algebras

KAZAN
FEDERAL UNIVERSITY

- RUS
- 中文
- ES

TOPOLOGICAL GRADING OF SEMIGROUP C*-ALGEBRAS

Form of presentation

Articles in Russian journals and collections

Year of publication

2020

Язык

английский

Authors, employees of KFU

Gumerov Renat Nelsonovich, author

Bibliographic description in the original language

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).

Annotation

Herald of the Bauman Moscow State Techical University

Keywords

grading, C*-algebra

The name of the journal

Herald of the Bauman Moscow State Techical University

URL

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

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=236809&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Gumerov Renat Nelsonovich	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/eng/?p_id=236809&p_lang=2	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	Articles in Russian journals and collections	ru_RU