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arXiv · 2003.01145

Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras

Philippe Meyer
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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 $ε$-orthogonal representation of an $ε$-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 Pandžić.

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Philippe Meyer. 2020-03-02. Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras. https://doi.org/10.1007/s00031-021-09680-x

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