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dc.contributor.author | Gumerov R.N. | |
dc.contributor.author | Lipacheva E.V. | |
dc.date.accessioned | 2021-02-25T20:47:03Z | |
dc.date.available | 2021-02-25T20:47:03Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 1812-3368 | |
dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/162392 | |
dc.description.abstract | © Author(s), 2020 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 o we construct the grading of a semigroup C*-algebra. To this aim the notion of the a-index of a monomial is introduced. This notion is the main tool in the construction of the grading. We make use of the a-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 Cf-algebra. | |
dc.relation.ispartofseries | Herald of the Bauman Moscow State Technical University, Series Natural Sciences | |
dc.subject | Cancellative semigroup | |
dc.subject | Grading | |
dc.subject | Monomial | |
dc.subject | Reduced semigroup C*-algebra | |
dc.subject | Topologically graded C*-algebra | |
dc.subject | σ-index | |
dc.title | Topological grading of semigroup C*-algebras | |
dc.type | Article | |
dc.relation.ispartofseries-issue | 90 | |
dc.collection | Публикации сотрудников КФУ | |
dc.relation.startpage | 44 | |
dc.source.id | SCOPUS18123368-2020-90-SID85090732107 |