The geometric classification of Leibniz algebras

Nurlan Ismailov; Ivan Kaygorodov; Yury Volkov

doi:10.1142/S0129167X18500350

The geometric classification of Leibniz algebras

Rings and Algebras 2021-01-20 v2 Algebraic Geometry

Authors: Nurlan Ismailov , Ivan Kaygorodov , Yury Volkov

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Abstract

We describe all rigid algebras and all irreducible components in the variety of four dimensional Leibniz algebras $\mathfrak{Leib}_4$ over $\mathbb{C}.$ In particular, we prove that the Grunewald--O'Halloran conjecture is not valid and the Vergne conjecture is valid for $\mathfrak{Leib}_4.$

Keywords

Leibniz algebras geometric classification rigid algebras irreducible components four dimensional Grunewald-O'Halloran conjecture Vergne conjecture

Cite

@article{arxiv.1705.04346,
  title  = {The geometric classification of Leibniz algebras},
  author = {Nurlan Ismailov and Ivan Kaygorodov and Yury Volkov},
  journal= {arXiv preprint arXiv:1705.04346},
  year   = {2021}
}

Comments

It is the correction of the published version. The classification of irreducible components and rigid algebras is improved. Namely, the algebra $\mathfrak{L}_{2}$ is not rigid

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