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

Abstract

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 $\mathbb{N}$. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7.

33 pages

References in corpus (2)

• A new invariant of quadratic Lie algebras
• Pseudo-euclidean Jordan algebras

Cited by in corpus (1)

• A classification of quadratic and odd quadratic Lie superalgebras in low dimensions