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Non-semisimple Lie algebras with Levi factor so(3), sl(2,R) and their invariants

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dc.contributor.authorCampoamor-Stursberg, Rutwig
dc.date.accessioned2023-06-20T10:36:09Z
dc.date.available2023-06-20T10:36:09Z
dc.date.issued2003
dc.description.abstractWe analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{% oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and \frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that for any dimension n >= 6 there exist Lie algebras \frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/22031
dc.identifier.citationGell-Mann M and Ne’eman Y 1964 The eightfold way (New York:Bejamin) Fomenko A and Trofimov V V 1988 Integrable systems on Lie algebras and symmetric spaces (New York: Gordon and Breach) Rosensteel G and Graber J L 2002 J. Phys. A:Math. Gen. 35 L535 Kirillov A A 1999 Bull. Am. Math. Soc. 36 433 Campoamor-Stursberg R 2002 J. Phys. A:Math. Gen. 35 6293 Ancochea J M and Campoamor-Stursberg R 2002 J. Pure Appl. Alg. 170 1 Cariñena J F, del Olmo M and Santander M 1981 J. Phys. A:Math. Gen. 14 1 Campoamor-Stursberg R 2002 Hadronic J. to appear Lohmus J and Tammelo R 1997 Hadronic J. 20 361 Bacry H and Lévy-Leblond J M 1968 J. Math. Phys. 9 1605 Beltrametti E G and Blasi A 1966 Phys. Lett. 20 62 Pauri M and Prosperi G M 1966 Nuovo Cimento 43 533 Racah G 1950 Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. 8 108 Lemke J, Ne’eman Y and Pecina-Cruz J N 1992 J. Math. Phys. 33 2656 Abellanas L and Alonso L M 1975 J. Math. Phys. 16 1580 Pecina-Cruz J N 1994 J. Math. Phys. 35 3146 Pauli W 1926 Z. Physik 36 336 Ndogmo J P 2000 J. Phys. A: Math. Gen. 33 2273 Patera J, Sharp R T, Winternitz P and Zassenhaus H 1976 J. Math. Phys. 17 986 Turkowski P 1988 Phys. Lett. B 207 36 Demianski M, Golda Z, Sokolowski L M, Slydlowoski M and Turkowski P 1987 J. Math. Phys. 28 171 Rand D, Winternitz P and Zassenhaus H 1988 Linear Alg. Appl. 109 197 Iwahori N 1959 Nagoya Math. J. 14 59 Turkowski P 1988 J. Geom. Phys. 4 119 Niederer U 1972 Helv. Phys. Acta 45 802 Dynkin E B 1952 Mat. Sbornik 30 349 Weimar-Woods E 1995 J. Math. Phys. 36 4519 Ait Abdelmalek, Leng X, Patera J and Winternitz P 1996 J. Phys. A: Math. Gen. 29 7519
dc.identifier.doi10.1088/0305-4470/36/5/312
dc.identifier.issn0305-4470
dc.identifier.officialurlhttp://arxiv.org/pdf/math/0208195v1.pdf
dc.identifier.relatedurlhttp://arxiv.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50729
dc.issue.number5
dc.journal.titleJournal of physics A: Mathematical and general
dc.language.isoeng
dc.page.final1369
dc.page.initial1357
dc.publisherIOP Publishing
dc.rights.accessRightsopen access
dc.subject.cdu512
dc.subject.ucmÁlgebra
dc.subject.unesco1201 Álgebra
dc.titleNon-semisimple Lie algebras with Levi factor so(3), sl(2,R) and their invariants
dc.typejournal article
dc.volume.number36
dspace.entity.typePublication
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