Pregled bibliografske jedinice broj: 542220
On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras
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:
Boris Širola
(autor)
Citiraj ovu publikaciju:
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