RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 3, Pages 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. 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.

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).


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

Full text: PDF file (219 kB)
References: PDF file   HTML file

Bibliographic databases:

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}


Linking options:
  • http://mi.mathnet.ru/eng/timm1555
  • http://mi.mathnet.ru/eng/timm/v24/i3/p98

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. V. M. Levchuk, G. S. Suleimanova, “Obobschenie zadachi A. I. Maltseva o kommutativnykh podalgebrakh na algebry Shevalle”, Chebyshevskii sb., 19:3 (2018), 231–240  mathnet  crossref  elib
    2. Galina S. Suleimanova, “The highest dimension of commutative subalgebras in Chevalley algebras”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 351–354  mathnet  crossref
    3. 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  mathnet  crossref
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:83
    Full text:18
    References:9
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021