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Non-solvable contractions of semisimple Lie algebras in low dimension

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dc.contributor.authorCampoamor-Stursberg, Rutwig
dc.date.accessioned2023-06-20T10:35:00Z
dc.date.available2023-06-20T10:35:00Z
dc.date.issued2007
dc.description.abstractThe 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
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Educación y Ciencia de España
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/21389
dc.identifier.citationSegal 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
dc.identifier.doi10.1088/1751-8113/40/20/008
dc.identifier.issn0305-4470
dc.identifier.officialurlhttp://iopscience.iop.org/1751-8121/40/20/008/
dc.identifier.relatedurlhttp://iopscience.iop.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50649
dc.issue.number20
dc.journal.titleJournal of physics A: Mathematical and general
dc.language.isoeng
dc.page.final5372
dc.page.initial5355
dc.publisherIOP Publishing
dc.relation.projectIDMTM2006-09152
dc.rights.accessRightsopen access
dc.subject.cdu512.554.3
dc.subject.keywordLie algebra
dc.subject.keywordcontraction
dc.subject.keyworddeformation
dc.subject.keywordLevi decomposition
dc.subject.ucmÁlgebra
dc.subject.unesco1201 Álgebra
dc.titleNon-solvable contractions of semisimple Lie algebras in low dimension
dc.typejournal article
dc.volume.number40
dspace.entity.typePublication
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