Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a Field
In 1905 I.~Shur pointed out the largest dimension of commutative subgroups in the groups $SL(n,\mathbb{C})$ and proved that for $n>3$ such the subgroups are automorphic to each other. In 1945 A.I.~Mal’tsev investigated the problem of description of the largest dimension commutative subgroups in t...
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doaj-4b1ae0972ef34fc58f145ac0b34365bc2020-11-24T21:58:52ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика" 1997-76702541-87852019-09-012913138https://doi.org/10.26516/1997-7670.2019.29.31Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a FieldF.M. KirillovaIn 1905 I.~Shur pointed out the largest dimension of commutative subgroups in the groups $SL(n,\mathbb{C})$ and proved that for $n>3$ such the subgroups are automorphic to each other. In 1945 A.I.~Mal’tsev investigated the problem of description of the largest dimension commutative subgroups in the simple complex Lie groups. He solved the problem by the transition to the complex Lie algebras and by the reduction to the same problem for the maximal nilpotent subalgebra. Let $N$ be a niltriangular subalgebra of a Chevalley algebra. The article deals with the problem of describing the largest dimension commutative subalgebras of $N$ over an arbitrary field. The solution of this problem is obtained for the subalgebra $N$ of $E_6$ type Chevalley algebra.http://mathizv.isu.ru/en/article/file?id=1307Chevalley algebraniltriangular subalgebralargest dimension commutative subalgebra |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
F.M. Kirillova |
spellingShingle |
F.M. Kirillova Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a Field Известия Иркутского государственного университета: Серия "Математика" Chevalley algebra niltriangular subalgebra largest dimension commutative subalgebra |
author_facet |
F.M. Kirillova |
author_sort |
F.M. Kirillova |
title |
Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a Field |
title_short |
Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a Field |
title_full |
Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a Field |
title_fullStr |
Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a Field |
title_full_unstemmed |
Generalized Reduced Mal'tsev Problem on Commutative Subalgebras of $E_6$ Type Chevalley Algebras over a Field |
title_sort |
generalized reduced mal'tsev problem on commutative subalgebras of $e_6$ type chevalley algebras over a field |
publisher |
Irkutsk State University |
series |
Известия Иркутского государственного университета: Серия "Математика" |
issn |
1997-7670 2541-8785 |
publishDate |
2019-09-01 |
description |
In 1905 I.~Shur pointed out the largest dimension of commutative
subgroups in the groups $SL(n,\mathbb{C})$ and proved that for $n>3$
such the subgroups are automorphic to each other. In 1945
A.I.~Mal’tsev investigated the problem of description of the largest
dimension commutative subgroups in the simple complex Lie groups. He
solved the problem by the transition to the complex Lie algebras and
by the reduction to the same problem for the maximal nilpotent
subalgebra. Let $N$ be a niltriangular subalgebra of a Chevalley
algebra. The article deals with the problem of describing the
largest dimension commutative subalgebras of $N$ over an arbitrary
field. The solution of this problem is obtained for the subalgebra
$N$ of $E_6$ type Chevalley algebra. |
topic |
Chevalley algebra niltriangular subalgebra largest dimension commutative subalgebra |
url |
http://mathizv.isu.ru/en/article/file?id=1307 |
work_keys_str_mv |
AT fmkirillova generalizedreducedmaltsevproblemoncommutativesubalgebrasofe6typechevalleyalgebrasoverafield |
_version_ |
1725850467505799168 |