On Vassiliev Invariants Not Coming from Semisimple Lie Algebras
نویسنده
چکیده
We prove a refinement of Vogel’s statement that the Vassiliev invariants of knots coming from semisimple Lie algebras do not generate all Vassiliev invariants. This refinement takes into account the second grading on the Vassiliev invariants induced by cabling of knots. As an application we get an amelioration of the actually known lower bounds for the dimensions of the space of Vassiliev invariants.
منابع مشابه
The number of primitive Vassiliev invariants up to degree twelve
We present algorithms giving upper and lower bounds for the number of independent primitive rational Vassiliev invariants of degree m modulo those of degree m − 1. The values have been calculated for the formerly unknown degrees m = 10, 11, 12. Upper and lower bounds coincide, which reveals that all Vassiliev invariants of degree ≤ 12 are orientation insensitive and are coming from representati...
متن کاملAlgebraic structures on modules of diagrams
There exists a graded algebra Λ acting in a natural way on many modules of 3valent diagrams. Every simple Lie superalgebra with a nonsingular invariant bilinear form induces a character on Λ. The classical and exceptional Lie algebras and the Lie superalgebra D(2, 1, α) produce eight distinct characters on Λ and eight distinct families of weight functions on chord diagrams. As a consequence we ...
متن کاملHomfly and Kauffman polynomials
We calculate the dimensions of the space of Vassiliev invariants coming from the Homfly polynomial of links, and of the space of Vassiliev invariants coming from the Kauffman polynomial of links. We show that the intersection of these spaces is spanned by the Vassiliev invariants coming from the Jones polynomial and from a polynomial called Υ. We also show that linearly independent Vassiliev in...
متن کاملSemi-direct Products of Lie Algebras, Their Invariants and Representations
Introduction 1 1. Preliminaries 6 2. Generic stabilisers (centralisers) for the adjoint representation 9 3. Generic stabilisers for the coadjoint representation 10 4. Semi-direct products of Lie algebras and modules of covariants 12 5. Generic stabilisers and rational invariants for semi-direct products 14 6. Reductive semi-direct products and their polynomial invariants 21 7. Takiff Lie algebr...
متن کاملVassiliev Invariants and the Loop States in Quantum Gravity
The purpose of this paper is to expose properties of Vassiliev invariants by using the simplest of the approaches to the functional integral definition of link invariants. These methods are strong enough to give the top row evaluations of Vassiliev invariants for the classical Lie algebras. They give an insight into the structure of these invariants without using the full perturbation expansion...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997