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

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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.
21 pages

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Representation Theory, K-Theory and Homology, Quantum Algebra, 14D15;13D10;14B12;16S80;16E40;17B55;17B56;17B70

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http://salesiana.dossiersoluciones.com/handle/123456789/66920

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303346
 http://arxiv.org/abs/math/0303346

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arXiv