Ad-nilpotent ideals of a parabolic 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 کاملNormalizers of ad-nilpotent ideals
Let g be a complex simple Lie algebra. Fix a Borel subalgebra b and a Cartan subalgebra t ⊂ b. The nilpotent radical of b is denoted by u. The corresponding set of positive (resp. simple) roots is ∆ (resp. Π). An ideal of b is called ad-nilpotent, if it is contained in [b, b]. The theory of ad-nilpotent ideals has attracted much recent attention in the work of Kostant, Cellini-Papi, Sommers, an...
متن کاملENUMERATION OF ad-NILPOTENT b-IDEALS FOR SIMPLE LIE ALGEBRAS
We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.
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: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.11.005