Cyclic Homology and Quantum Orbits
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Cyclic Homology and Quantum Orbits
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| Creator |
Maszczyk, T.
Sütlü, S. |
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| 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.
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| Date |
2019-02-13T16:47:03Z
2019-02-13T16:47:03Z 2015 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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