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Hopf algebras for ternary algebras

Abstract : We construct a universal enveloping algebra associated with the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincaré–Birkhoff–Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters of the transformation of a Lie algebra of order of 3. It turns out that these variables are the variables which generate the three-exterior algebra.
keyword : Lie algebras
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Submitted on : Monday, July 20, 2009 - 4:28:53 PM
Last modification on : Friday, May 8, 2020 - 1:09:38 AM

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M. Goze, M. Rausch de Traubenberg. Hopf algebras for ternary algebras. Journal of Mathematical Physics, American Institute of Physics (AIP), 2009, 50, pp.063508. ⟨10.1063/1.3152631⟩. ⟨in2p3-00405649⟩



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