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

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2018, Volume 24, Number 3, Pages 98–108
DOI: https://doi.org/10.21538/0134-4889-2018-24-3-98-108 (Mi timm1555)

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. Kirillova^a, G. S. Suleimanova^b

^a Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
^b Khakas Technical Institute

Full-text PDF (219 kB) Citations (3)

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DOI: https://doi.org/10.21538/0134-4889-2018-24-3-98-108

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.

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

Received: 10.06.2018

Bibliographic databases:

Document Type: Article

UDC: 512.554.3

MSC: 17B05, 17B30

Language: Russian

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}

Linking options:

https://www.mathnet.ru/eng/timm1555

https://www.mathnet.ru/eng/timm/v24/i3/p98

This publication is cited in the following 3 articles:

Galina S. Suleimanova, “The highest dimension of commutative subalgebras in Chevalley algebras”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 351–354
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
V. M. Levchuk, G. S. Suleimanova, “Obobschenie zadachi A. I. Maltseva o kommutativnykh podalgebrakh na algebry Shevalle”, Chebyshevskii sb., 19:3 (2018), 231–240

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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