|
|
|
The Kontsevich integral and quantized Lie superalgebras
Nathan Geer
|
|
Algebraic & Geometric Topology 5
(2005) 1111–1139
|
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).
|
Keywords
Vassiliev invariants, weight system,
Kontsevich integral, Lie superalgebras, Links–Gould
invariant, quantum invariants
|
Mathematical Subject Classification
Primary: 57M27
Secondary: 17B37, 17B65
|
Publication
Received: 6 May 2005
Accepted: 15 August 2005
Published: 11 September 2005
|
|
