Hopf algebras for ternary algebras

Details Hopf algebras for ternary algebras Hopf algebras for ternary algebras

2008-09-24

arxiv.org/abs/0809.4212v2

J. Math. Phys. 50 (2009) 063508

Physics

Mathematical Physics

21 pages

Scientific paper

We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincar\'e-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 three. It turns out that these variables are the variables which generate the three-exterior algebra.

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