Enumeration of ad-Nilpotent b-Ideals for Simple Lie Algebras
نویسندگان
چکیده
منابع مشابه
ENUMERATION 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 کاملCombinatorial Analogues of Ad-nilpotent Ideals for Untwisted Affine Lie Algebras
We study certain types of ideals in the standard Borel subalgebra of an untwisted affine Lie algebra. We classify these ideals in terms of the root combinatorics and give an explicit formula for the number of such ideals in type A. The formula involves various aspects of combinatorics of Dyck paths and leads to a new interesting integral sequence.
متن کاملSimple completable contractions of nilpotent Lie algebras
We study a certain class of non-maximal rank contractions of the nilpotent Lie algebra gm and show that these contractions are completable Lie algebras. As a consequence a family of solvable complete Lie algebras of non-maximal rank is given in arbitrary dimension. . AMS Math. Subj. Class. 17B10, 17B30.
متن کاملSome properties of nilpotent Lie algebras
In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.
متن کاملInvariant Prime Ideals in Quantizations of Nilpotent Lie Algebras
De Concini, Kac and Procesi defined a family of subalgebras U + of a quantized universal enveloping algebra Uq(g), associated to the elements of the corresponding Weyl group W . They are deformations of the universal enveloping algebras U(n+ ∩ Adw(n−)) where n± are the nilradicals of a pair of dual Borel subalgebras. Based on results of Gorelik and Joseph and an interpretation of U + as quantiz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2002
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0792