Geodesic
The highest dimension of commutative subalgebras in Chevalley algebras
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 351-354

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Let $L_\Phi(K)$ denotes a Chevalley algebra with the root system $\Phi$ over a field $K$. In 1945 A. I. Mal'cev investigated the problem of describing abelian subgroups of highest dimension in complex simple Lie groups. He solved this problem by transition to complex Lie algebras and by reduction to the problem of describing commutative subalgebras of highest dimension in the niltriangular subalgebra. Later these methods were modified and applied for the problem of describing large abelian subgroups in finite Chevalley groups. The main result of this article allows to calculate the highest dimension of commutative subalgebras in a Chevalley algebra $L_\Phi (K)$ over an arbitrary field.
Keywords: Chevalley algebra
Mots-clés : commutative subalgebra. 
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     title = {The highest dimension of commutative subalgebras in {Chevalley} algebras},
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Galina S. Suleimanova. The highest dimension of commutative subalgebras in Chevalley algebras. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 351-354. http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a9/