Quantum link invariant from the Lie superalgebra D2 1,α

Patureau-Mirand, Bertrand

doi:10.2140/agt.2006.6.329

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Quantum link invariant from the Lie superalgebra ${\mathfrak D}_{2 1,\alpha}$

Bertrand Patureau-Mirand

Algebraic & Geometric Topology 6 (2006) 329–349

DOI: 10.2140/agt.2006.6.329

arXiv: math.GT/0404548

Abstract

The usual construction of link invariants from quantum groups applied to the superalgebra $D_{2 1, α}$ is shown to be trivial. One can modify this construction to get a two variable invariant. Unusually, this invariant is additive with respect to connected sum or disjoint union. This invariant contains an infinity of Vassiliev invariants that are not seen by the quantum invariants coming from Lie algebras (so neither by the colored HOMFLY-PT nor by the colored Kauffman polynomials).

Keywords

finite type invariants, quantum groups, Lie superalgebra

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27, 17B37

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Publication

Received: 1 February 2005

Accepted: 15 August 2005

Published: 12 March 2006

Authors

Bertrand Patureau-Mirand
LMAM Université de Bretagne-Sud Centre de Recherche Campus de Tohannic BP 573 F-56017 Vannes France
http://www.univ-ubs.fr/lmam/patureau/

Volume 6, issue 1 (2006)