Versal Deformations of Three Dimensional Lie Algebras as L-infinity Algebras

Details Versal Deformations of Three Dimensional Lie Algebras as L-infinity Algebras Versal Deformations of Three Dimensional Lie Algebras as L-infinity Algebras

2003-03-27

arxiv.org/abs/math/0303346v1

Mathematics

Representation Theory

21 pages

Scientific paper

We consider versal deformations of 0|3-dimensional L-infinity algebras, which correspond precisely to ordinary (non-graded) three dimensional Lie algebras. The classification of such algebras over C is well known, although we shall give a derivation of this classification using an approach of treating them as L-infinity algebras. Because the symmetric algebra of a three dimensional odd vector space contains terms only of exterior degree less than or equal to three, the construction of versal deformations can be carried out completely. We give a characterization of the moduli space of Lie algebras using deformation theory as a guide to understanding the picture.

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