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## Open Mathematics

2011 | 9 | 6 | 1317-1332
Tytuł artykułu

### Normalizers and self-normalizing subgroups II

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Treść / Zawartość
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EN
Abstrakty
EN
Let $\mathbb{K}$ be a field, G a reductive algebraic $\mathbb{K}$-group, and G 1 ≤ G a reductive subgroup. For G 1 ≤ G, the corresponding groups of $\mathbb{K}$-points, we study the normalizer N = N G(G 1). In particular, for a standard embedding of the odd orthogonal group G 1 = SO(m, $\mathbb{K}$) in G = SL(m, $\mathbb{K}$) we have N ≅ G 1 ⋊ µm($\mathbb{K}$), the semidirect product of G 1 by the group of m-th roots of unity in $\mathbb{K}$. The normalizers of the even orthogonal and symplectic subgroup of SL(2n, $\mathbb{K}$) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof in the odd orthogonal case to be completed here. Also, for G = GL(m, $\mathbb{K}$) and G 1 = O(m, $\mathbb{K}$) we have N ≅ G 1 ⋊ $\mathbb{K}$ ×. In both of these cases, N is a self-normalizing subgroup of G.
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
1317-1332
Opis fizyczny
Daty
wydano
2011-12-01
online
2011-09-23
Twórcy
autor
• University of Zagreb
Bibliografia
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•  Širola B., Pairs of Lie algebras and their self-normalizing reductive subalgebras, J. Lie Theory, 2009, 19(4), 735–766
•  Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)
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