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Pregled bibliografske jedinice broj: 542220

On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras


Širola, Boris
On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras // Proceedings of the American Mathematical Society, 141 (2013), 7; 2233-2243 doi:10.1090/S0002-9939-2013-11508-X (međunarodna recenzija, članak, znanstveni)


CROSBI ID: 542220 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

Naslov
On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras

Autori
Širola, Boris

Izvornik
Proceedings of the American Mathematical Society (0002-9939) 141 (2013), 7; 2233-2243

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Pair of Lie algebras; semisimple Lie algebra; reductive subalgebra; Cartan subalgebra; Cartan subspace; Cartan pair

Sažetak
Let (g, g_1) be a pair of Lie algebras, defined over a field of characteristic zero, where g is semisimple and g_1 is a subalgebra reductive in g. We prove a result giving a necessary and sufficient technical condition so that the following holds: (Q1) For any Cartan subalgebra $h_1\subseteq g_1$ there exists a unique Cartan subalgebra $h\subseteq g$ containing h_1. Next we study a class of pairs (g, g_1), satisfying (Q1), that we call Cartan pairs. For such pairs, and the corresponding Cartan subspaces, we prove some useful results that are classical for symmetric pairs. Thus we extend a part of the previous research on Cartan subspaces done by Dixmier, Lepowsky and McCollum.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekti:
037-0372781-2811 - Omotačke algebre Liejevih algebri i njihovi moduli (Širola, Boris, MZOS ) ( CroRIS)

Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Profili:

Avatar Url Boris Širola (autor)

Poveznice na cjeloviti tekst rada:

doi www.ams.org dx.doi.org

Citiraj ovu publikaciju:

Širola, Boris
On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras // Proceedings of the American Mathematical Society, 141 (2013), 7; 2233-2243 doi:10.1090/S0002-9939-2013-11508-X (međunarodna recenzija, članak, znanstveni)
Širola, B. (2013) On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras. Proceedings of the American Mathematical Society, 141 (7), 2233-2243 doi:10.1090/S0002-9939-2013-11508-X.
@article{article, author = {\v{S}irola, Boris}, year = {2013}, pages = {2233-2243}, DOI = {10.1090/S0002-9939-2013-11508-X}, keywords = {Pair of Lie algebras, semisimple Lie algebra, reductive subalgebra, Cartan subalgebra, Cartan subspace, Cartan pair}, journal = {Proceedings of the American Mathematical Society}, doi = {10.1090/S0002-9939-2013-11508-X}, volume = {141}, number = {7}, issn = {0002-9939}, title = {On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras}, keyword = {Pair of Lie algebras, semisimple Lie algebra, reductive subalgebra, Cartan subalgebra, Cartan subspace, Cartan pair} }
@article{article, author = {\v{S}irola, Boris}, year = {2013}, pages = {2233-2243}, DOI = {10.1090/S0002-9939-2013-11508-X}, keywords = {Pair of Lie algebras, semisimple Lie algebra, reductive subalgebra, Cartan subalgebra, Cartan subspace, Cartan pair}, journal = {Proceedings of the American Mathematical Society}, doi = {10.1090/S0002-9939-2013-11508-X}, volume = {141}, number = {7}, issn = {0002-9939}, title = {On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras}, keyword = {Pair of Lie algebras, semisimple Lie algebra, reductive subalgebra, Cartan subalgebra, Cartan subspace, Cartan pair} }

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka::


  • MathSciNet


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