E.A. Kirillova, G.S. Suleimanova. Highest dimension commutative ideals of a niltriangular subalgebra of a Chevalley algebra over a field P. ... 98-108

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.

Keywords: Chevalley algebra, niltriangular subalgebra, commutative ideals and highest dimension ideals

The paper was received by the Editorial Office on Juny 10, 2018.

Funding Agency: This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00707).

Evgeniya Alekseevna Kirillova, doctoral student, Siberian Federal University, Krasnoyarsk, 660041 Russia, e-mail: kea92@bk.ru

Galina Safiullanovna Suleimanova, Dr. Phys.-Math. Sci., Khakas Technical Institute — Branch of Siberian Federal University, Abakan, 655017 Russia, e-mail: suleymanova@list.ru


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