English

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.

Keywords

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

R2 v1 2026-06-21T22:06:57.953Z