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Degenerations of Jordan Algebras and ''Marginal'' Algebras

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arxiv 1707.08836 v2 pith:JLLOE5XI submitted 2017-07-24 math.RA

Ilya Gorshkov , Ivan Kaygorodov , Yury Popov This is my paper · ORCID
classification math.RA
keywords algebrasjordanmarginalalternativedegenerationsdescribejordmathfrak
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abstract

We describe all degenerations of the variety $\mathfrak{Jord}_3$ of Jordan algebras of dimension three over $\mathbb{C}.$ In particular, we describe all irreducible components in $\mathfrak{Jord}_3.$ For every $n$ we define an $n$-dimensional rigid ''marginal'' Jordan algebra of level one. Also, we discuss ''marginal'' algebras in associative, alternative, left alternative, non-commutative Jordan, Leibniz, and anticommutative cases.

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Cited by 1 Pith paper

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  1. Varieties of Nilpotent Lie Superalgebras of dimension $\leq 5$

    math.RA 2019-08 conditional novelty 7.0 of 10

    The nilpotent Lie superalgebras of dimension at most five are classified, their degenerations and irreducible components are found, and rigid nilpotent Lie superalgebras are constructed in every dimension.

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