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Pregled bibliografske jedinice broj: 411182

Pairs of Lie algebras and their self-normalizing reductive subalgebras


Širola, Boris
Pairs of Lie algebras and their self-normalizing reductive subalgebras // Journal of lie theory, 19 (2009), 4; 735-766 (međunarodna recenzija, članak, znanstveni)


CROSBI ID: 411182 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

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:

Avatar Url Boris Širola (autor)

Citiraj ovu publikaciju:

Širola, Boris
Pairs of Lie algebras and their self-normalizing reductive subalgebras // Journal of lie theory, 19 (2009), 4; 735-766 (međunarodna recenzija, članak, znanstveni)
Širola, B. (2009) Pairs of Lie algebras and their self-normalizing reductive subalgebras. Journal of lie theory, 19 (4), 735-766.
@article{article, author = {\v{S}irola, Boris}, year = {2009}, pages = {735-766}, keywords = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Self-normalizing subalgebra, Principal nilpotent element, Principal TDS, Trivial extension}, journal = {Journal of lie theory}, volume = {19}, number = {4}, issn = {0949-5932}, title = {Pairs of Lie algebras and their self-normalizing reductive subalgebras}, keyword = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Self-normalizing subalgebra, Principal nilpotent element, Principal TDS, Trivial extension} }
@article{article, author = {\v{S}irola, Boris}, year = {2009}, pages = {735-766}, keywords = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Self-normalizing subalgebra, Principal nilpotent element, Principal TDS, Trivial extension}, journal = {Journal of lie theory}, volume = {19}, number = {4}, issn = {0949-5932}, title = {Pairs of Lie algebras and their self-normalizing reductive subalgebras}, keyword = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Self-normalizing subalgebra, Principal nilpotent element, Principal TDS, Trivial extension} }

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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