#### Volume 6, issue 1 (2006)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Quantum link invariant from the Lie superalgebra ${\mathfrak D}_{2 1,\alpha}$

### Bertrand Patureau-Mirand

Algebraic & Geometric Topology 6 (2006) 329–349
 arXiv: math.GT/0404548
##### Abstract

The usual construction of link invariants from quantum groups applied to the superalgebra ${\mathfrak{D}}_{2\phantom{\rule{0.3em}{0ex}}1,\alpha }$ 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
##### 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/