The Kontsevich integral and quantized Lie superalgebras
نویسنده
چکیده
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). AMS Classification 57M27; 17B65, 17B37
منابع مشابه
The Kontsevich Integral And
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 super...
متن کاملThe Kontsevich Integral and Re-normalized Link Invariants Arising from Lie Superalgebras
We show that the coefficients of the re-normalized link invariants of [3] are Vassiliev invariants which give rise to a canonical family of weight systems.
متن کاملOn Defining Relations of the Affine Lie Superalgebras and Their Quantized Universal Enveloping Superalgebras
Introduction. In this paper, we give defining relations of the affine Lie superalgebras and defining relations of a super-version of the Drinfeld[D1]Jimbo[J] affine quantized enveloping algebras. As a result, we can exactly define the affine quantized universal enveloping superalgebras with generators and relations. Moreover we give a Drinfeld’s realization of Uh(ŝl(m|n)). For the Kac-Moody Lie...
متن کاملEtingof-kazhdan Quantization of Lie Superbialgebras
For every semi-simple Lie algebra g one can construct the DrinfeldJimbo algebra U h (g). This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U h (g), Drinfeld used the KZ-equations to construct a quasi-Hopf algebra Ag . He proved that particular categories of modules over the algebras U h (g) and Ag are tensor equivalent. Analogo...
متن کاملLocally finite basic classical simple Lie superalgebras
In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.
متن کامل