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2005 The Kontsevich integral and quantized Lie superalgebras
Nathan Geer
Algebr. Geom. Topol. 5(3): 1111-1139 (2005). DOI: 10.2140/agt.2005.5.1111

Abstract

Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: 1) quantum group invariants using the R–matrix, 2) the Kontsevich universal link invariant followed by the Lie algebra based weight system. Le and Murakami showed that these two link invariants are the same. These constructions can be generalized to some classes of Lie superalgebras. In this paper we show that constructions 1) and 2) give the same invariants for the Lie superalgebras of type A–G. We use this result to investigate the Links–Gould invariant. We also give a positive answer to a conjecture of Patureau-Mirand’s concerning invariants arising from the Lie superalgebra D(2,1;α).

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Nathan Geer. "The Kontsevich integral and quantized Lie superalgebras." Algebr. Geom. Topol. 5 (3) 1111 - 1139, 2005. https://doi.org/10.2140/agt.2005.5.1111

Information

Received: 6 May 2005; Accepted: 15 August 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1118.57014
MathSciNet: MR2171805
Digital Object Identifier: 10.2140/agt.2005.5.1111

Subjects:
Primary: 57M27
Secondary: 17B37, 17B65

Rights: Copyright © 2005 Mathematical Sciences Publishers

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