Pregled bibliografske jedinice broj: 741235
Compatible pairs of Borel subalgebras and shared orbit pairs
Compatible pairs of Borel subalgebras and shared orbit pairs // Journal of algebra, 423 (2015), 726-766 doi:10.1016/j.jalgebra.2014.10.035 (međunarodna recenzija, članak, znanstveni)
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Naslov
Compatible pairs of Borel subalgebras and shared orbit pairs
Autori
Širola, Boris
Izvornik
Journal of algebra (0021-8693) 423
(2015);
726-766
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; shared orbit pair; nilpotent element; nilpotent orbit
Sažetak
Consider a class of pairs (g, g_1), where g is a semisimple Lie algebra and g_1 is a subalgebra reductive in g, satisfying the following: For any Cartan subalgebra h_1 in g_1 there is a unique Cartan subalgebra h in g containing h_1. Given such a pair (g, g_1) and a Borel subalgebra b_1 in g_1 we study a (finite) set S_{; ; ; Bor}; ; ; ^g(b_1) of all Borel subalgebras b in g containing b_1. In particular we point at the subclass of pairs (g, g_1) when S_{; ; ; Bor}; ; ; ^g(b_1) is a singleton, for every Borel subalgebra b_1 in g_1. As a consequence, for such pairs we relate the corresponding flag varieties B(g) and B(g_1). As an interesting class of pairs (g, g_1), for which we can apply our results on pairs of Borel subalgebras, we study in detail the pairs considered by R. Brylinski and B. Kostant related to shared orbit pairs.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
037-0372781-2811 - Omotačke algebre Liejevih algebri i njihovi moduli (Širola, Boris, MZOS ) ( CroRIS)
HRZZ-IP-2013-11-2634 - Algebarske i kombinatorne metode u teoriji verteks algebri (ACMVAT) (Adamović, Dražen, HRZZ - 2013-11) ( 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
- Zentrallblatt für Mathematik/Mathematical Abstracts