Publication: Non-solvable contractions of semisimple Lie algebras in low dimension
Loading...
Official URL
Full text at PDC
Publication Date
2007
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
IOP Publishing
Citations
Exportar
Abstract
The problem of non-solvable contractions of Lie algebras is analyzed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras of dimension n ≤ 8, and obtain the non-solvable contractions of the latter class of algebras
Description
UCM subjects
Unesco subjects
Keywords
Citation
Segal I E 1951 Duke Math. J 18 221
Inönü E and Wigner E P 1953 Proc. Natl. Acad. Sci. U.S. 39 510
Saletan E 1961 J. Math. Phys. 2 1
Kupczynski M 1969 Comm. Math. Phys. 13 154
Satyanarayana M V 1986 J. Phys. A: Math. Gen. 19 3697
Weimar-Woods E 1991 J. Math. Phys. 32 2028
Levy-Nahas M 1967 J. Math. Phys. 8 1211
Richardson R W and Page S 1967 Trans. Amer. Math. Soc. 127 302
Conatser C W 1972 J. Math. Phys. 13 196
Huddleston P L 1978 J. Math. Phys. 19 1645
Nesterenko I and Popovych R I 2007 J. Math. Phys. 47 123515
Nijenhuis A and Richardson R W 1966 Bull. Amer. Math. Soc. 72 1
Hochschild G and Serre J-P 1953 Ann. Math. 57 591
Vilela Mendes R 1994 J. Phys. A: Math. Gen. 27 8091
de Azcárraga J A and Izquierdo J M 1995 Lie Groups, Lie Algebras, Cohomology and some Applications to Physics (Cambridge: Cambridge Univ. Press)
Chryssomalakos C and Okon E 2004 Int. J. Mod. Phys. D 13 1817
Weimar-Woods E 2000 Rev. Math. Phys. 12 1505
Campoamor-Stursberg R 2007 Phys. Lett. A to appear
Tolpygo A K 1972 Mat. Zametki 42 251
Campoamor-Stursberg R 2003 Acta Physica Polonica B 34 3901
Turkowski P 1988 J. Math. Phys. 29 2139
Campoamor-Stursberg R 2005 J. Phys. A: Math. Gen. 38 4187
Herranz F J and Santander M 1997 J. Phys. A: Math. Gen. 30 5411
Herranz F J, Perez Bueno J C and Santander M 1998 J. Phys. A: Math. Gen. 31 5327
Campoamor-Stursberg R 2006 J. Phys. A: Math. Gen. 39 2325
Weimar E 1972 Lett. Nuovo Cimento 4 43
Onishchik A L 2003 Lectures on Real Semisimple Lie Algebras and Their Representations (Zürich:European Math. Soc.)
Cornwell J F 1984 Group Theory in Physics (New York: Academic Press)
Bacry H and Nuyts J 1986 J. Math. Phys. 27 2455
Campoamor-Stursberg R 2004 Phys. Lett. A 327 138
Cariñena J F, Grabowski J and Marmo G 2001 J. Phys. A: Math. Gen. 34 3769
Guillemin V and Sternberg S 1984 Symplectic Techniques in Physics (N.Y.: Cambridge Univ.Press)
Sternberg S 1975 Trans. Amer. Math. Soc. 212 113
Bolsinov A V 1985 Trudy Sem. Vektor. Tenzor. Anal. 22 8
Winternitz P 1998 Phys. Atomic Nuclei 61 1705