Abelian Ideals of a Borel Subalgebra and Root Systems, II
نویسندگان
چکیده
منابع مشابه
Abelian Ideals of a Borel Subalgebra and Long Positive Roots
Let b be a Borel subalgebra of a simple Lie algebra g. Let Ab denote the set of all Abelian ideals of b. It is easily seen that any a ∈ Ab is actually contained in the nilpotent radical of b. Therefore a is determined by the the corresponding set of roots. More precisely, let t be a Cartan subalgebra of g lying in b and let ∆ be the root system of the pair (g, t). Choose ∆, the system of positi...
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A well-known Peterson’s theorem says that the number of abelian ideals in a Borel subalgebra of a rank-r finite dimensional simple Lie algebra is exactly 2r . In this paper, we determine the dimensional distribution of abelian ideals in a Borel subalgebra of finite dimensional simple Lie algebras, which is a refinement of the Peterson’s theorem capturing more Lie algebra invariants.
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2019
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-019-09902-7