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Pregled bibliografske jedinice broj: 344758

Pairs of semisimple Lie algebras and their maximal reductive subalgebras


Širola, Boris
Pairs of semisimple Lie algebras and their maximal reductive subalgebras // Algebras and Representation Theory, 11 (2008), 3; 233-250 doi:10.1007/s10468-007-9068-z (međunarodna recenzija, članak, znanstveni)


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Naslov
Pairs of semisimple Lie algebras and their maximal reductive subalgebras

Autori
Širola, Boris

Izvornik
Algebras and Representation Theory (1386-923X) 11 (2008), 3; 233-250

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

Ključne riječi
Pair of Lie algebras; Semisimple Lie algebra; Reductive subalgebra; Cartan subalgebra; Self-normalizing subalgebra; Finite-order automorphism; Fixed point algebra

Sažetak
Let g be a semisimple Lie algebra over a field K, char(K)=0, and g_1 a subalgebra reductive in g. Suppose that the restriction of the Killing form B of g to g_1xg_1 is nondegenerate. Consider the following statements: (1) For any Cartan subalgebra h_1 of g_1 there is a unique Cartan subalgebra h of g containing h_1 ; (2) g_1 is self-normalizing in g ; (3) The B-orthogonal p of g_1 in g is simple as a g_1-module for the adjoint representation. We give some answers to this natural question: For which pairs (g, g_1) do (1), (2) or (3) hold? We also study how p in general decomposes as a g_1-module, and when g_1 is a maximal subalgebra of g. In particular suppose (g, sigma) is a pair with g as above and sigma its automorphism of order m. Assume that K contains a primitive m-th root of unity. Define g_1:=g^sigma, the fixed point algebra for sigma. We prove the following generalization of a well known result for symmetric Lie algebras, i.e., for m=2: (a) (g, g_1) satisfies (1) ; (b) For m prime, (g, g_1) satisfies (2).

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)

Poveznice na cjeloviti tekst rada:

doi www.springerlink.com

Citiraj ovu publikaciju:

Širola, Boris
Pairs of semisimple Lie algebras and their maximal reductive subalgebras // Algebras and Representation Theory, 11 (2008), 3; 233-250 doi:10.1007/s10468-007-9068-z (međunarodna recenzija, članak, znanstveni)
Širola, B. (2008) Pairs of semisimple Lie algebras and their maximal reductive subalgebras. Algebras and Representation Theory, 11 (3), 233-250 doi:10.1007/s10468-007-9068-z.
@article{article, author = {\v{S}irola, Boris}, year = {2008}, pages = {233-250}, DOI = {10.1007/s10468-007-9068-z}, keywords = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Cartan subalgebra, Self-normalizing subalgebra, Finite-order automorphism, Fixed point algebra}, journal = {Algebras and Representation Theory}, doi = {10.1007/s10468-007-9068-z}, volume = {11}, number = {3}, issn = {1386-923X}, title = {Pairs of semisimple Lie algebras and their maximal reductive subalgebras}, keyword = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Cartan subalgebra, Self-normalizing subalgebra, Finite-order automorphism, Fixed point algebra} }
@article{article, author = {\v{S}irola, Boris}, year = {2008}, pages = {233-250}, DOI = {10.1007/s10468-007-9068-z}, keywords = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Cartan subalgebra, Self-normalizing subalgebra, Finite-order automorphism, Fixed point algebra}, journal = {Algebras and Representation Theory}, doi = {10.1007/s10468-007-9068-z}, volume = {11}, number = {3}, issn = {1386-923X}, title = {Pairs of semisimple Lie algebras and their maximal reductive subalgebras}, keyword = {Pair of Lie algebras, Semisimple Lie algebra, Reductive subalgebra, Cartan subalgebra, Self-normalizing subalgebra, Finite-order automorphism, Fixed point algebra} }

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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