Pregled bibliografske jedinice broj: 411182
Pairs of Lie algebras and their self-normalizing reductive subalgebras
Pairs of Lie algebras and their self-normalizing reductive subalgebras // Journal of lie theory, 19 (2009), 4; 735-766 (međunarodna recenzija, članak, znanstveni)
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Naslov
Pairs of Lie algebras and their self-normalizing reductive subalgebras
Autori
Širola, Boris
Izvornik
Journal of lie theory (0949-5932) 19
(2009), 4;
735-766
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Pair of Lie algebras; Semisimple Lie algebra; Reductive subalgebra; Self-normalizing subalgebra; Principal nilpotent element; Principal TDS; Trivial extension
Sažetak
We consider a class P of pairs (g, g_1) of K-Lie algebras $g_1\subseteq g$ satisfying certain "rigidity conditions" ; here K is a field of characteristic 0, and g_1 is reductive. We provide some further evidence that P contains a number of nonsymmetric pairs that are worth studying ; e.g., in some branching problems, and for the purposes of the geometry of orbits. In particular, for an infinite series (g, g_1)=(sl(n+1), sl(2)) we show that it is in P, and precisely describe a g_1-module structure of the Killing-orthogonal p(n) of g_1 in g. Using this and the Kostant's philosophy concerning the exponents for (complex) Lie algebras, we obtain two more results. First ; suppose K is algebraically closed, g is semisimple all of whose factors are classical, and s is a principal TDS. Then (g, s) belongs to P. Second ; suppose (g, g_1) is a pair satisfying certain condition (C), and there exists a semisimple $s\subseteq g_1$ such that (g, s) is from P (e.g., s is a principal TDS). Then (g, g_1) is from P as well. Finally, given a pair (g, g_1), we have some useful observations concerning the relationship between the coadjoint orbits corresponding to g and g_1, respectively.
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