On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup
The class of С*-algebras generated by the elementary inverse semigroup and being deformations of the Toeplitz algebra has been introduced and studied. The properties of these algebras have been investigated. All their irreducible representations and automorphism groups have been described. These alg...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2016-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | http://kpfu.ru/portal/docs/F2032277858/158_2_phys_mat_3.pdf |
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| _version_ | 1846144021649424384 |
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| author | S.A. Grigoryan E.V. Lipacheva |
| author_facet | S.A. Grigoryan E.V. Lipacheva |
| author_sort | S.A. Grigoryan |
| collection | DOAJ |
| description | The class of С*-algebras generated by the elementary inverse semigroup and being deformations of the Toeplitz algebra has been introduced and studied. The properties of these algebras have been investigated. All their irreducible representations and automorphism groups have been described. These algebras have been proved to be Z-graded С*-algebras. For a certain class of algebras in the family under consideration the compact quantum semigroup structure has been constructed. |
| format | Article |
| id | doaj-art-8b4c5c3f94ed43adb42790583b178823 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2016-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-8b4c5c3f94ed43adb42790583b1788232024-12-02T09:09:27ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982016-06-011582180193On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse SemigroupS.A. Grigoryan0E.V. Lipacheva1Kazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaThe class of С*-algebras generated by the elementary inverse semigroup and being deformations of the Toeplitz algebra has been introduced and studied. The properties of these algebras have been investigated. All their irreducible representations and automorphism groups have been described. These algebras have been proved to be Z-graded С*-algebras. For a certain class of algebras in the family under consideration the compact quantum semigroup structure has been constructed.http://kpfu.ru/portal/docs/F2032277858/158_2_phys_mat_3.pdfС*-algebraToeplitz algebrairreducible representationinverse semigroupautomorphism groupcompact quantum semigroup |
| spellingShingle | S.A. Grigoryan E.V. Lipacheva On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup Учёные записки Казанского университета: Серия Физико-математические науки С*-algebra Toeplitz algebra irreducible representation inverse semigroup automorphism group compact quantum semigroup |
| title | On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup |
| title_full | On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup |
| title_fullStr | On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup |
| title_full_unstemmed | On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup |
| title_short | On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup |
| title_sort | on the structure of с algebras generated by representations of the elementary inverse semigroup |
| topic | С*-algebra Toeplitz algebra irreducible representation inverse semigroup automorphism group compact quantum semigroup |
| url | http://kpfu.ru/portal/docs/F2032277858/158_2_phys_mat_3.pdf |
| work_keys_str_mv | AT sagrigoryan onthestructureofsalgebrasgeneratedbyrepresentationsoftheelementaryinversesemigroup AT evlipacheva onthestructureofsalgebrasgeneratedbyrepresentationsoftheelementaryinversesemigroup |