Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras
Representation Theory
2023-11-28 v1 Rings and Algebras
Abstract
The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a necessary and sufficient condition to construct a colour Lie algebra from an -orthogonal representation of an -quadratic colour Lie algebra. This is used to prove a strange Freudenthal-de Vries formula for basic colour Lie algebras as well as a Parthasarathy formula for cubic Dirac operators of colour Lie algebras. We calculate the cohomology induced by this Dirac operator, analogously to the algebraic Vogan conjecture proved by Huang and Pand\v{z}i\'c.
Keywords
Cite
@article{arxiv.2003.01145,
title = {Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras},
author = {Philippe Meyer},
journal= {arXiv preprint arXiv:2003.01145},
year = {2023}
}