Formal deformations, contractions and moduli spaces of Lie algebras

Details Formal deformations, contractions and moduli spaces of Lie algebras Formal deformations, contractions and moduli spaces of Lie algebras

2007-02-09

arxiv.org/abs/math/0702268v1

Mathematics

Quantum Algebra

27 pages

Scientific paper

10.1007/s10773-007-9481-4

Jump deformations and contractions of Lie algebras are inverse concepts, but the approaches to their computations are quite different. In this paper, we contrast the two approaches, showing how to compute jump deformations from the miniversal deformation of a Lie algebra, and thus arrive at the contractions. We also compute contractions directly. We use the moduli spaces of real 3-dimensional and complex 3 and 4-dimensional Lie algebras as models for explaining a deformation theory approach to computation of contractions.

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