Highest dimension commutative ideals of a niltriangular subalgebra of a Chevalley algebra over a field

E. A. Kirillova ; G. S. Suleimanova

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 98-108

Résumé

Let $N$ be a niltriangular subalgebra of a Chevalley algebra. We study the problem of describing commutative ideals of $N$ of the highest dimension over an arbitrary field. It is proved that $N$ contains a commutative ideal of this dimension, and all such ideals are found. In addition, all maximal commutative ideals of $N$ are described for the types $G_2$ and $F_4$. As a consequence, the highest dimension of commutative subalgebras in all subalgebras of $N$ is found.

Détail

Keywords: Chevalley algebra, commutative ideals and highest dimension ideals.
Mots-clés : niltriangular subalgebra

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