Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cubic Dirac operators and the strange Freudenthal-de Vries formula for
  colour Lie algebras   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 $\epsilon$-orthogonal representation of an
$\epsilon$-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.

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The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci