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arXiv · 1209.3832

ad-Nilpotent positively-graded Borel module subalgebras

Tim Ridenour·Adam Sandler
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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.

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Tim Ridenour, Adam Sandler. 2012-09-18. ad-Nilpotent positively-graded Borel module subalgebras. https://arxiv.org/abs/1209.3832

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