Cyclic Homology and Quantum Orbits
A natural isomorphism between the cyclic object computing the relative cyclic homology of a homogeneous quotient-coalgebra-Galois extension, and the cyclic object computing the cyclic homology of a Galois coalgebra with SAYD coefficients is presented. The isomorphism can be viewed as the cyclic-homo...
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| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147108 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Cyclic Homology and Quantum Orbits / T. Maszczyk, S. Sütlü // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 40 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1471082019-02-14T01:26:45Z Cyclic Homology and Quantum Orbits Maszczyk, T. Sütlü, S. A natural isomorphism between the cyclic object computing the relative cyclic homology of a homogeneous quotient-coalgebra-Galois extension, and the cyclic object computing the cyclic homology of a Galois coalgebra with SAYD coefficients is presented. The isomorphism can be viewed as the cyclic-homological counterpart of the Takeuchi-Galois correspondence between the left coideal subalgebras and the quotient right module coalgebras of a Hopf algebra. A spectral sequence generalizing the classical computation of Hochschild homology of a Hopf algebra to the case of arbitrary homogeneous quotient-coalgebra-Galois extensions is constructed. A Pontryagin type self-duality of the Takeuchi-Galois correspondence is combined with the cyclic duality of Connes in order to obtain dual results on the invariant cyclic homology, with SAYD coefficients, of algebras of invariants in homogeneous quotient-coalgebra-Galois extensions. The relation of this dual result with the Chern character, Frobenius reciprocity, and inertia phenomena in the local Langlands program, the Chen-Ruan-Brylinski-Nistor orbifold cohomology and the Clifford theory is discussed. 2015 Article Cyclic Homology and Quantum Orbits / T. Maszczyk, S. Sütlü // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 40 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 19D55; 57T15; 06A15; 46A20 DOI:10.3842/SIGMA.2015.041 http://dspace.nbuv.gov.ua/handle/123456789/147108 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A natural isomorphism between the cyclic object computing the relative cyclic homology of a homogeneous quotient-coalgebra-Galois extension, and the cyclic object computing the cyclic homology of a Galois coalgebra with SAYD coefficients is presented. The isomorphism can be viewed as the cyclic-homological counterpart of the Takeuchi-Galois correspondence between the left coideal subalgebras and the quotient right module coalgebras of a Hopf algebra. A spectral sequence generalizing the classical computation of Hochschild homology of a Hopf algebra to the case of arbitrary homogeneous quotient-coalgebra-Galois extensions is constructed. A Pontryagin type self-duality of the Takeuchi-Galois correspondence is combined with the cyclic duality of Connes in order to obtain dual results on the invariant cyclic homology, with SAYD coefficients, of algebras of invariants in homogeneous quotient-coalgebra-Galois extensions. The relation of this dual result with the Chern character, Frobenius reciprocity, and inertia phenomena in the local Langlands program, the Chen-Ruan-Brylinski-Nistor orbifold cohomology and the Clifford theory is discussed. |
| format |
Article |
| author |
Maszczyk, T. Sütlü, S. |
| spellingShingle |
Maszczyk, T. Sütlü, S. Cyclic Homology and Quantum Orbits Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Maszczyk, T. Sütlü, S. |
| author_sort |
Maszczyk, T. |
| title |
Cyclic Homology and Quantum Orbits |
| title_short |
Cyclic Homology and Quantum Orbits |
| title_full |
Cyclic Homology and Quantum Orbits |
| title_fullStr |
Cyclic Homology and Quantum Orbits |
| title_full_unstemmed |
Cyclic Homology and Quantum Orbits |
| title_sort |
cyclic homology and quantum orbits |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147108 |
| citation_txt |
Cyclic Homology and Quantum Orbits / T. Maszczyk, S. Sütlü // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 40 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT maszczykt cyclichomologyandquantumorbits AT sutlus cyclichomologyandquantumorbits |
| first_indexed |
2023-05-20T17:26:36Z |
| last_indexed |
2023-05-20T17:26:36Z |
| _version_ |
1796153297180033024 |