ad-nilpotent ideals of a Borel subalgebra III
P. Cellini (Univ. di Chieti-Pescara), P. Papi (Univ. di Roma "La, Sapienza")
TL;DR
This paper investigates the structure of ad-nilpotent ideals within a Borel subalgebra, providing a uniform formula for the dimensions of maximal ideals and extending previous analyses of abelian ideals.
Contribution
It introduces a uniform formula for maximal ideal dimensions and completes the analysis of ad-nilpotent ideals initiated in earlier works.
Findings
Derived a uniform formula for the dimension of maximal ideals
Analyzed the poset structure of abelian ideals
Extended previous results on ad-nilpotent ideals
Abstract
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 \cite{CP2}, \cite{CP3}.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry