CUBIC DIRAC OPERATORS AND THE STRANGE FREUDENTHAL–DE VRIES FORMULA FOR COLOUR LIE ALGEBRAS
Keyword(s):
De Vries
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AbstractThe 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.
2016 ◽
Vol 16
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pp. 1750162
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pp. 1250011
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pp. 1950028
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pp. 115-131
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pp. 2764-2775
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