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arXiv · 2103.11977

Gradings on the algebra of triangular matrices as a Lie algebra: revisited

Plamen Koshlukov·Felipe Yukihide Yasumura
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Abstract

We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a complete classification of isomorphism classes of the gradings. We also provide a classification of the practical isomorphism classes of the gradings, which is a better alternative way to consider these gradings up to being essentially the same object. Finally, we investigate in details the case where the characteristic of the base field is $2$, a topic that was neglected in previous works.

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Plamen Koshlukov, Felipe Yukihide Yasumura. 2021-03-22. Gradings on the algebra of triangular matrices as a Lie algebra: revisited. https://arxiv.org/abs/2103.11977

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