The Kontsevich Integral and Re-normalized Link Invariants Arising from Lie Superalgebras
نویسنده
چکیده
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.
منابع مشابه
The Kontsevich integral and quantized Lie superalgebras
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
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 کامل1 S ep 2 00 6 MULTIVARIABLE LINK INVARIANTS ARISING FROM LIE SUPERALGEBRAS OF TYPE I
This paper generalize [7]: We construct new links in-variants from g, a type I basic classical Lie superalgebra. The construction uses the existence of an unexpected replacement of the vanishing quantum dimension of typical module. Using this, we get a multivariable link invariant associated to any one parameter family of irreducible g-modules.
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 کاملVassiliev Theory
There exists a natural filtration on the module freely generated by knots (or links). This filtration is called the Vassiliev filtration and has many nice properties. In particular every quotient of this filtration is finite dimensional. A knot invariant which vanishes on some module of this filtration is called a Vassiliev invariant. Almost every knot invariant defined in algebraic term can be...
متن کامل