Cover Image

On the sum of two Lie algebras with finite-dimensional commutants

We prove that an infinite-dimensional Lie algebra over an arbitrary field which is decomposable into the sum of two of its subalgebras with finite-dimensional commutants is almost solvable.

Saved in:

Bibliographic Details
Date:	1995
Main Authors:	Petravchuk, A. P., Петравчук, А. П.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 1995
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/5505
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

On the sum of an almost abelian Lie algebra and a Lie algebra finite-dimensional over its center
by: Petravchuk, A. P., et al.
Published: (1999)

Lie algebras, expanded into the sum of Abelian and nilpotent subalgebras
by: Petravchuk , A. P., et al.
Published: (1988)

On Strongly Inert Subalgebras of an Infinite-Dimensional Lie Algebra
by: Petravchuk, A. P., et al.
Published: (2002)

Finite-dimensional subalgebras in polynomial Lie algebras of rank one
by: Arzhantsev, I. V., et al.
Published: (2011)

Finite-dimensional subalgebras in polynomial Lie algebras of rank one
by: Arzhantsev, I.V., et al.
Published: (2011)

Lie algebras associated with modules over polynomial rings
by: Petravchuk, A. P., et al.
Published: (2017)

Monogenic functions in finite-dimensional commutative associative algebras
by: V. S. Shpakivskyi
Published: (2015)

Constructive description of monogenic functions in finite dimensional commutative algebras
by: V. S. Shpakivskyi
Published: (2015)

On nilpotent Lie algebras of derivations of fraction fields
by: Petravchuk, A.P.
Published: (2016)

On nilpotent Lie algebras of derivations of fraction fields
by: Petravchuk, Anatoliy P.
Published: (2016)

Monogenic functions in two dimensional commutative algebras to equations of plane orthotropy
by: C. V. Hryshchuk
Published: (2018)

Closed polynomials and saturated subalgebras of polynomial algebras
by: Arzhantsev, I. V., et al.
Published: (2007)

Lie algebras associated with modules over polynomial rings
by: A. P. Petravchuk, et al.
Published: (2017)

On sum of a nilpotent and an ideally finite algebras
by: Bilun, Svitlana V.
Published: (2018)

The Virasoro Algebra and Some Exceptional Lie and Finite Groups
by: Tuite, M.P.
Published: (2007)

Centralizers of elements in Lie algebras of derivations of fields
by: S. V. Lysenko, et al.
Published: (2015)

Solvable Lie algebras of derivations of polynomial rings in three variables
by: Chapovskyi, Ie. Yu.; Чаповський І. Є.; Київський національний університет ім. Тараса Шевченка, Київ, et al.
Published: (2018)

Lie algebras of derivations with large abelian ideals
by: Klymenko, I. S., et al.
Published: (2019)

Lie algebras of derivations with large abelian ideals
by: Klymenko, I.S., et al.
Published: (2019)

Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups
by: Sushchansky, V.I., et al.
Published: (2005)

Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
by: Accardi, L., et al.
Published: (2009)

Locally nilpotent Lie algebras of derivations of integral domains
by: A. P. Petravchuk, et al.
Published: (2017)

Criteria Conceived Commutative Hypercomplex Number Systems Direct Sum of Low-Dimensional Systems
by: Kalinovsky, J. А.
Published: (2012)

On the Auslander algebra of one commutative semigroup of finite representation type
by: O. V. Zubaruk
Published: (2020)

Solvable Lie algebras of derivations of polynomial rings in three variables
by: Ie. Yu. Chapovskyi, et al.
Published: (2018)

Discrete models on one-dimensional net with the preset Lie algebra of symmetries
by: Balinsky , A. I., et al.
Published: (1992)

Unitary subgroups of commutative group algebras of characteristic two
by: Zh. Baloh, et al.
Published: (2020)

Unitary subgroups of commutative group algebras of characteristic two
by: Laver, V., et al.
Published: (2020)

Structure of Finite-Dimensional Nodal Algebras
by: V. V. Zembik
Published: (2014)

Structure of Finite-Dimensional Nodal Algebras
by: Zembyk, V. V., et al.
Published: (2014)

The central polynomials for the finite dimensional Grassmann algebras
by: Koshlukov, P., et al.
Published: (2009)

On Two-Dimensional Model Representations of One Class of Commuting Operators
by: Hatamleh, R., et al.
Published: (2014)

On the Group $C^{*}$-Algebras of a Semidirect Product of Commutative and Finite Groups
by: Samoilenko, Yu. S., et al.
Published: (2005)

Leibniz Algebras and Lie Algebras
by: Mason, G., et al.
Published: (2013)

Three-dimensional Lie algebras for a one class of wave equations
by: O. V. Mahda
Published: (2017)

On two-dimensional model representations of one class of commuting operators
by: Hatamleh, R., et al.
Published: (2014)

On Two-Dimensional Model Representations of One Class of Commuting Operators
by: R. Hatamleh, et al.
Published: (2014)

Алгебры Ли, разложимые в сумму абелевой и нильпотентной подалгебр
by: Петравчук, А.П.
Published: (1988)

О сумме почти абелевой алгебры Ли и алгебры Ли, конечномерной над своимцешром
by: Петравчук, А.П.
Published: (1999)

О сильно инертных подалгебрах бесконечномерной алгебры Ли
by: Петравчук, А.П.
Published: (2002)