On linear resolvability of universal quantum dimensions

  title={On linear resolvability of universal quantum dimensions},
  author={M. Y. Avetisyan and R. L. Mkrtchyan},
  journal={Journal of Knot Theory and Its Ramifications},
In the study of finite (Vassiliev’s) knot invariants, Vogel introduced the so-called universal parameters, belonging to the projective plane, in particular parametrizing the simple Lie algebras by Vogel’s table. Subsequently, a number of quantities, such as some universal knot invariants and (quantum) dimensions of simple Lie algebras, have been represented in terms of these parameters, i.e., in the universal form. We prove that at the points from Vogel’s table all known universal quantum… 

Tables from this paper


On (ad)n(X2)k series of universal quantum dimensions
We present a universal, in Vogel’s sense, expression for the quantum dimension of the Cartan product of arbitrary powers of the adjoint and X2 representations of simple Lie algebras. The same formula
On universal knot polynomials
A bstractWe present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these
On the Road Map of Vogel’s Plane
We define “population” of Vogel’s plane as points for which universal character of adjoint representation is regular in the finite plane of its argument. It is shown that they are given exactly by
A universal dimension formula for complex simple Lie algebras
We present a universal formula for the dimension of the Cartan powers of the adjoint representation of a complex simple Lie algebra (i.e., a universal formula for the Hilbert functions of homogeneous
In this paper we first give three known examples of strict pivotal categories defined by a finite presentation. Then in the final section we give some of the relations for a conjectural strict
Universality in Chern-Simons theory
A bstractWe show that the perturbative part of the partition function in the ChernSimons theory on a 3-sphere as well as the central charge and expectation value of the unknotted Wilson loop in the
Sextonions and the Magic Square
Associated to any complex simple Lie algebra is a non‐reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square
Computational evidence for Deligne's conjecture regarding exceptional Lie groups
Pour j ≤ 4, on obtient pour tous les groupes exceptionnels une decomposition uniforme de la puissance tensorielle j-ieme de la representation adjointe, en accord avec les conjectures de Deligne [1].
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)