A maximal cubic quotient of the braid algebra
Geometric Topology
2018-11-14 v1 Quantum Algebra
Representation Theory
Abstract
We study a quotient of the group algebra of the braid group in which the Artin generators satisfy a cubic relation. This quotient is maximal among the ones satisfying such a cubic relation. It is finite-dimensional for at least n at most 5 and we investigate its module structure in this range. We also investigate the proper quotients of it that appear in the realm of quantum groups, and describe another maximal quotient related to the usual Hecke algebras. Finally, we describe the connection between this algebra and a quotient of the algebra of horizontal chord diagrams introduced by Vogel. We prove that these two are isomorphic for n at most 5.
Keywords
Cite
@article{arxiv.1811.04964,
title = {A maximal cubic quotient of the braid algebra},
author = {Ivan Marin},
journal= {arXiv preprint arXiv:1811.04964},
year = {2018}
}