Conformal representations of Leibniz algebras

Details Conformal representations of Leibniz algebras Conformal representations of Leibniz algebras

2007-08-17

arxiv.org/abs/0708.2315v1

Mathematics

Rings and Algebras

misc. note to arXiv:math/0611501

Scientific paper

In this note we present a more detailed and explicit exposition of the definition of a conformal representation of a Leibniz algebra. Recall (arXiv:math/0611501v3) that Leibniz algebras are exactly Lie dialgebras. The idea is based on the general fact that every dialgebra that belongs to a variety $\Var $ can be embedded into a conformal algebra of the same variety. In particular, we prove that an arbitrary (finite dimensional) Leibniz algebra has a (finite) faithful conformal representation. As a corollary, we deduce the analogue of the PBW-theorem for Leibniz algebras.

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