Degenerations of Jordan Algebras and ''Marginal'' Algebras

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.

arXiv admin note: text overlap with arXiv:1611.06454

References in corpus (6)

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• Degenerations of Zinbiel and nilpotent Leibniz algebras
• The algebraic and geometric classification of nilpotent Novikov algebras
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Cited by in corpus (6)

• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent Novikov algebras
• Degenerations of Jordan Superalgebras
• Non-associative algebraic structures: classification and structure
• On the Kantor product, II
• Varieties of Nilpotent Lie Superalgebras of dimension $\le 5$