Degenerations of pre-Lie algebras
Rings and Algebras
2008-09-15 v1
Abstract
We consider the variety of pre-Lie algebra structures on a given n-dimensional vector space. The group GL_n(K) acts on it, and we study the closure of the orbits with respect to the Zariski topology. This leads to the definition of pre-Lie algebra degenerations. We give fundamental results on such degenerations, including invariants and necessary degeneration criteria. We demonstrate the close relationship to Lie algebra degenerations. Finally we classify all orbit closures in the variety of complex 2-dimensional pre-Lie algebras.
Cite
@article{arxiv.0809.2188,
title = {Degenerations of pre-Lie algebras},
author = {Dietrich Burde and Thomas Beneš},
journal= {arXiv preprint arXiv:0809.2188},
year = {2008}
}