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In this paper we give a re-normalization of the Reshetikhin-Turaev quantum invariants of links, by modified quantum dimensions. In the case of simple Lie algebras these modified quantum dimensions are proportional to the usual quantum dimensions. More interestingly we will give two examples where the usual quantum dimensions vanish but the modified quantum… (More)
For every semi-simple Lie algebra g one can construct the Drinfeld-Jimbo algebra U DJ h (g). This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U DJ h (g), Drin-feld used the KZ-equations to construct a quasi-Hopf algebra Ag. He proved that particular categories of modules over the algebras… (More)
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… (More)
In this paper we construct new links invariants from a type I basic Lie superalgebra g. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical module, by non-trivial " fake quantum dimensions. " Using this, we get a multivariable link invariant associated to any one parameter family of irreducible… (More)
In this paper we use the Etingof-Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld-Jimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that the D-J type superalgebra associated to a Lie superalgebra of type A-G, with the distinguished Cartan matrix, is… (More)
In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of sl(2|1) is trivial. However, we modify this construction and define a nontrivial link invariant. This new invariant can be… (More)
We show how to define invariants of graphs related to quantum sl 2 when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions.
The famous Drinfeld-Kohno theorem for simple Lie algebras states that the monodromy representation of the Knizhnik-Zamolodchikov equations for these Lie algebras expresses explicitly via R-matrices of the corresponding Drinfeld-Jimbo quantum groups. This result was generalized by the second author to simple Lie superalgebras of type A-G. In this paper, we… (More)
In this paper we give a re-normalization of the su-pertrace on the category of representations of Lie superalgebras of type I, by a kind of modified superdimension. The genuine superdimensions and supertraces are generically zero. However, these modified superdimensions are non-zero and lead to a kind of supertrace which is non-trivial and invariant. As an… (More)
We show that the coefficients of the re-normalized link invariants of  are Vassiliev invariants which give rise to a canon-ical family of weight systems.