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Pregled bibliografske jedinice broj: 741244

Distinguished nilpotent orbits, Kostant pairs and normalizers of Lie algebras


Širola, Boris
Distinguished nilpotent orbits, Kostant pairs and normalizers of Lie algebras // Journal of algebra, 423 (2015), 636-682 doi:10.1016/j.jalgebra.2014.10.036 (međunarodna recenzija, članak, znanstveni)


Naslov
Distinguished nilpotent orbits, Kostant pairs and normalizers of Lie algebras

Autori
Širola, Boris

Izvornik
Journal of algebra (0021-8693) 423 (2015); 636-682

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

Ključne riječi
Semisimple Lie algebra; Cartan subalgebra; root; root system; Borel subalgebra; pair of Lie algebras; Kostant pair; normalizer; self-normalizing subalgebra; nilpotent element; distinguished nilpotent element; nilpotent orbit

Sažetak
A pair of Lie algebras (g, g_1) will be called a Kostant pair if g is semisimple, g_1 is reductive in g and the restriction of the Killing form B_g to g_1 is nondegenerate. We study the class of such (nonsymmetric) pairs and obtain some useful and new structural results. We study the structure of the normalizers N_g(g_1), and as a consequence we obtain some corresponding worthy results about algebraic groups. In particular we consider an interesting case when g_1 is a distinguished sl_2-subalgebra of g. Conmbined with the research due to V. L. Popov we observe that the notions of self-normalizing (reductive) subalgebras of a semisimple Lie algebra and projective self-dual algebraic subvarieties of the usual nilpotent cones are closely related.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
037-0372781-2811 - Omotačke algebre Liejevih algebri i njihovi moduli (Boris Širola, )
HRZZ-IP-2013-11-2634 - Algebarske i kombinatorne metode u teoriji verteks algebri (Dražen Adamović, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:
Boris Širola, (160983)

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
  • Zentrallblatt für Mathematik/Mathematical Abstracts


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