B-Stable Ideals in the Nilradical of a Borel Subalgebra
نویسندگان
چکیده
منابع مشابه
ad-NILPOTENT IDEALS OF A BOREL SUBALGEBRA III
This paper is devoted to a detailed study of certain remarkable posets which form a natural partition of all abelian ideals of a Borel subalgebra. Our main result is a nice uniform formula for the dimension of maximal ideals in these posets. We also obtain results on ad-nilpotent ideals which complete the analysis started in [CP2], [CP3].
متن کاملad-NILPOTENT IDEALS OF A BOREL SUBALGEBRA II
We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra g and the orbits of Q̌/(h + 1)Q̌ under the Weyl group (Q̌ being the coroot lattice and h the Coxeter number of g). From this result we deduce in a uniform way a counting formula for the ad-nilpotent ideals.
متن کاملAbelian 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...
متن کاملAbelian ideals in a Borel subalgebra of a complex simple Lie algebra
Let g be a complex simple Lie algebra and b a fixed Borel subalgebra of g. We shall describe the abelian ideals of b in a uniform way, that is, independent of the classification of complex simple Lie algebras.
متن کامل∨ ) ∈ ∈ , - fuzzy Lie subalgebra and ideals
generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries....
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2005
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2005-043-4