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Logarithmic Hennings
invariants for restricted quantum ${\mathfrak{sl}}(2)$
Anna Beliakova, Christian Blanchet and Nathan Geer |
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Algebraic & Geometric Topology 18 (2018) 4329–4358
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Abstract |
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We construct a Hennings-type logarithmic invariant for restricted quantum at a root of unity. This quantum group is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a –manifold and a colored link inside . The link is split into two parts colored by central elements and by trace classes, or elements in the Hochschild homology of , respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of , and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami. |
Keywords
quantum invariants, links, Hopf algebras, quantum Groups
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 17B37, 57M25
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References |
Publication
Received: 10 April 2018
Accepted: 7 June 2018
Published: 11 December 2018
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Authors |
| Anna Beliakova | |
| Institut für Mathematik Universität Zürich Zurich Switzerland |
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| Christian Blanchet | |
| Institut de Mathématiques de Jussieu
- Paris Rive Gauche Université Paris 7 (Denis Diderot) Paris France |
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| Nathan Geer | |
| Department of Mathematics and
Statistics Utah State University Logan, UT United States |
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