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 |
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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 |
|