Degenerations of pre-Lie algebras

Details Degenerations of pre-Lie algebras Degenerations of pre-Lie algebras

2008-09-12

arxiv.org/abs/0809.2188v1

Mathematics

Rings and Algebras

Scientific paper

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.

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