ad-Nilpotent positively-graded Borel module subalgebras
Representation Theory
2012-09-21 v2
Abstract
In this paper, we study certain ad-nilpotent subalgebras contained in the non-zero graded portion of a simple Z_n-graded Lie algebra. These subalgebras respect the grading on the Lie algebra and are modules for a Borel subalgebra for the grade-zero Lie subalgebra. We show that semisimple elements in such subalgebras lie in the center of the subalgebra, and we provide a classification of these subalgebras whose weight space decompositions have only non-zero weights.
Cite
@article{arxiv.1209.3832,
title = {ad-Nilpotent positively-graded Borel module subalgebras},
author = {Tim Ridenour and Adam Sandler},
journal= {arXiv preprint arXiv:1209.3832},
year = {2012}
}
Comments
v2. References added, 12 pages