Contractions of low-dimensional Lie algebras
Abstract
Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for both the complex and real Lie algebras of dimensions not greater than 4 are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and colevels of low-dimensional Lie algebras are discussed in detail. Properties of multiparametric and repeated contractions are also investigated.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- December 2006
- DOI:
- 10.1063/1.2400834
- arXiv:
- arXiv:math-ph/0608018
- Bibcode:
- 2006JMP....47l3515N
- Keywords:
-
- 03.65.Fd;
- 02.10.Ud;
- Algebraic methods;
- Linear algebra;
- Mathematical Physics;
- 17B05;
- 17B81
- E-Print:
- 47 pages, 4 figures, revised version