A characterization of stable and Borel ideals
โ Scribed by Maria Grazia Marinari; Luciana Ramella
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 244 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0938-1279
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๐ SIMILAR VOLUMES
We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra g and the orbits of Q/(h + 1) Q under the Weyl group ( Q 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-n
We present several naturally defined ฯ-ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set-theoretic properties of such ฯ-ideals.
Let a = {a 1 a 2 โข โข โข a n } be a sequence of integers or โ. We introduce a-stable ideals in a polynomial ring and study their homological properties. Our results generalize results on square-free monomial ideals by Aramova, Avramov, Herzog, Hibi, and Srinivasan.