Geometric classification of nilpotent Jordan algebras of dimension five

Maria Eugenia Martin; Iryna Kashuba

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arXiv · 1609.05594

Geometric classification of nilpotent Jordan algebras of dimension five

Maria Eugenia Martin·Iryna Kashuba

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Abstract

The variety $JorN_{5}$ of five-dimensional nilpotent Jordan algebras structures over an algebraically closed field is investigated. We show that $JorN_{5}$ is the union of five irreducible components, four of them correspond to the Zariski closure of the $GL_5$-orbits of four rigid algebras and the other one is the Zariski closure of an union of orbits of infinite family of algebras, none of them being rigid.

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Maria Eugenia Martin, Iryna Kashuba. 2016-09-19. Geometric classification of nilpotent Jordan algebras of dimension five. https://arxiv.org/abs/1609.05594

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