RT Journal Article T1 Non-solvable contractions of semisimple Lie algebras in low dimension A1 Campoamor-Stursberg, Rutwig AB 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 PB IOP Publishing SN 0305-4470 YR 2007 FD 2007 LK https://hdl.handle.net/20.500.14352/50649 UL https://hdl.handle.net/20.500.14352/50649 LA eng NO Segal I E 1951 Duke Math. J 18 221Inönü E and Wigner E P 1953 Proc. Natl. Acad. Sci. U.S. 39 510Saletan E 1961 J. Math. Phys. 2 1Kupczynski M 1969 Comm. Math. Phys. 13 154Satyanarayana M V 1986 J. Phys. A: Math. Gen. 19 3697Weimar-Woods E 1991 J. Math. Phys. 32 2028Levy-Nahas M 1967 J. Math. Phys. 8 1211Richardson R W and Page S 1967 Trans. Amer. Math. Soc. 127 302Conatser C W 1972 J. Math. Phys. 13 196Huddleston P L 1978 J. Math. Phys. 19 1645Nesterenko I and Popovych R I 2007 J. Math. Phys. 47 123515Nijenhuis A and Richardson R W 1966 Bull. Amer. Math. Soc. 72 1Hochschild G and Serre J-P 1953 Ann. Math. 57 591Vilela Mendes R 1994 J. Phys. A: Math. Gen. 27 8091de 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 1817Weimar-Woods E 2000 Rev. Math. Phys. 12 1505Campoamor-Stursberg R 2007 Phys. Lett. A to appearTolpygo A K 1972 Mat. Zametki 42 251Campoamor-Stursberg R 2003 Acta Physica Polonica B 34 3901Turkowski P 1988 J. Math. Phys. 29 2139Campoamor-Stursberg R 2005 J. Phys. A: Math. Gen. 38 4187Herranz F J and Santander M 1997 J. Phys. A: Math. Gen. 30 5411Herranz F J, Perez Bueno J C and Santander M 1998 J. Phys. A: Math. Gen. 31 5327Campoamor-Stursberg R 2006 J. Phys. A: Math. Gen. 39 2325Weimar E 1972 Lett. Nuovo Cimento 4 43Onishchik 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 2455Campoamor-Stursberg R 2004 Phys. Lett. A 327 138Cariñena J F, Grabowski J and Marmo G 2001 J. Phys. A: Math. Gen. 34 3769Guillemin V and Sternberg S 1984 Symplectic Techniques in Physics (N.Y.: Cambridge Univ.Press)Sternberg S 1975 Trans. Amer. Math. Soc. 212 113Bolsinov A V 1985 Trudy Sem. Vektor. Tenzor. Anal. 22 8Winternitz P 1998 Phys. Atomic Nuclei 61 1705 NO Ministerio de Educación y Ciencia de España DS Docta Complutense RD 28 nov 2023