Geometric classification of nilpotent Jordan algebras of dimension five

Maria Eugenia Martin; Iryna Kashuba

Geometric classification of nilpotent Jordan algebras of dimension five

Rings and Algebras 2016-09-20 v1

Authors: Maria Eugenia Martin , Iryna Kashuba

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.

Keywords

nilpotent Jordan algebras geometric classification irreducible components Zariski closure rigid algebras GL_5-orbits algebraic variety

Cite

@article{arxiv.1609.05594,
  title  = {Geometric classification of nilpotent Jordan algebras of dimension five},
  author = {Maria Eugenia Martin and Iryna Kashuba},
  journal= {arXiv preprint arXiv:1609.05594},
  year   = {2016}
}

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