منابع مشابه
Filtrations in Semisimple Lie Algebras, Ii
In this paper, we continue our study of the maximal bounded Z-filtrations of a complex semisimple Lie algebra L. Specifically, we discuss the functionals which give rise to such filtrations, and we show that they are related to certain semisimple subalgebras of L of full rank. In this way, we determine the “order” of these functionals and count them without the aid of computer computations. The...
متن کاملFiltrations in Semisimple Lie Algebras, III
This is the third in a series of papers. The first two, by Yiftach Barnea and this author, study the maximal bounded Z-filtrations of the finitedimensional simple Lie algebras over the complex numbers. Those papers obtain a complete characterization for all but the five exceptional Lie algebras, namely the ones of type G2, F4, E6, E7 and E8. Here, we fill in the missing step for the algebra G2....
متن کاملFiltrations in Semisimple Lie Algebras, I
In this paper, we study the maximal bounded Z-filtrations of a complex semisimple Lie algebra L. Specifically, we show that if L is simple of classical type An, Bn, Cn or Dn, then these filtrations correspond uniquely to a precise set of linear functionals on its root space. We obtain partial, but not definitive, results in this direction for the remaining exceptional algebras. Maximal bounded ...
متن کاملStructure Theory of Semisimple Lie Algebras II
3. The restriction K|gα×g−α , i.e. K(a, b) with a ∈ gα and b ∈ g−α, is non-degenerate, so it induces a pairing between gα and g−α. In particular, we have dim gα = dim g−α. 4. The restriction K|h×h is non-degenerate, hence we have an isomorphism ν : h → h∗ given by ν(h)(h′) = K(h, h′) for all h, h′ ∈ h. The map ν induces a bilinear form on h∗ by K(α, β) = β ( ν−1(α) ) = α ( ν−1(β) ) for all α, β...
متن کاملSmall Semisimple Subalgebras of Semisimple Lie Algebras
The goal of Section 2 is to provide a proof of Theorem 2.0.1. Section 3 introduces the necessary facts about Lie algebras and representation theory, with the goal being the proof of Proposition 3.5.7 (ultimately as an application of Theorem 2.0.1), and Proposition 3.3.1. In Section 4 we prove the main theorem, using Propositions 3.3.1 and 3.5.7. In Section 5, we apply the theorem to the special...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-04224-9