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This article is cited in 3 scientific papers (total in 3 papers)
Highest dimension commutative ideals of a niltriangular subalgebra of a Chevalley algebra over a field
E. A. Kirillovaa, G. S. Suleimanovab
a Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
b Khakas Technical Institute
Abstract:
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.
DOI:
https://doi.org/10.21538/0134-4889-2018-24-3-98-108
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UDC:
512.554.3
MSC: 17B05, 17B30
Received: 10.06.2018
Citation:
E. A. Kirillova, G. S. Suleimanova, “Highest dimension commutative ideals of a niltriangular subalgebra of a Chevalley algebra over a field”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 3, 2018, 98–108
Citation in format AMSBIB
\Bibitem{KirSul18}
\by E.~A.~Kirillova, G.~S.~Suleimanova
\paper Highest dimension commutative ideals of a niltriangular subalgebra of a Chevalley algebra over a field
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 3
\pages 98--108
\mathnet{http://mi.mathnet.ru/timm1555}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-3-98-108}
\elib{https://elibrary.ru/item.asp?id=35511280}
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This publication is cited in the following articles:
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V. M. Levchuk, G. S. Suleimanova, “Obobschenie zadachi A. I. Maltseva o kommutativnykh podalgebrakh na algebry Shevalle”, Chebyshevskii sb., 19:3 (2018), 231–240
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Galina S. Suleimanova, “The highest dimension of commutative subalgebras in Chevalley algebras”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 351–354
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E. A. Kirillova, “Generalized reduced Mal'tsev problem on commutative subalgebras of $E_6$ type Chevalley algebras over a field”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 29 (2019), 31–38
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