Jordanian double extensions of a quadratic vector space and symmetric Novikov algebras

Details Jordanian double extensions of a quadratic vector space and symmetric Novikov algebras Jordanian double extensions of a quadratic vector space and symmetric Novikov algebras

2010-12-27

arxiv.org/abs/1012.5556v1

Physics

Mathematical Physics

33 pages

Scientific paper

First, we study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra. We give an isomorphic characterization of 2-step nilpotent pseudo-Euclidean Jordan algebras. Next, we find a Jordan-admissible condition for a Novikov algebra $\N$. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7.

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