Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras

In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra morphisms from g to Out ( h ) . The...

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Main Authors:	Lina Song, Rong Tang
Format:	Article
Language:	English
Published:	MDPI AG 2017-12-01
Series:	Symmetry
Subjects:	Hom-Lie algebras derivations non-abelian extensions obstruction classes
Online Access:	https://www.mdpi.com/2073-8994/9/12/297

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spelling	doaj-5fad77be515c46b0aacd1c21812b58772020-11-24T22:05:33ZengMDPI AGSymmetry2073-89942017-12-0191229710.3390/sym9120297sym9120297Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie AlgebrasLina Song0Rong Tang1Department of Mathematics, Jilin University, Changchun 130012, ChinaDepartment of Mathematics, Jilin University, Changchun 130012, ChinaIn this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra morphisms from g to Out ( h ) . Then for a general Hom-Lie algebra morphism from g to Out ( h ) , we construct a cohomology class as the obstruction of existence of a non-abelian extension that induces the given Hom-Lie algebra morphism.https://www.mdpi.com/2073-8994/9/12/297Hom-Lie algebrasderivationsnon-abelian extensionsobstruction classes
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Lina Song Rong Tang
spellingShingle	Lina Song Rong Tang Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras Symmetry Hom-Lie algebras derivations non-abelian extensions obstruction classes
author_facet	Lina Song Rong Tang
author_sort	Lina Song
title	Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras
title_short	Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras
title_full	Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras
title_fullStr	Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras
title_full_unstemmed	Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras
title_sort	cohomology characterizations of diagonal non-abelian extensions of regular hom-lie algebras
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2017-12-01
description	In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra morphisms from g to Out ( h ) . Then for a general Hom-Lie algebra morphism from g to Out ( h ) , we construct a cohomology class as the obstruction of existence of a non-abelian extension that induces the given Hom-Lie algebra morphism.
topic	Hom-Lie algebras derivations non-abelian extensions obstruction classes
url	https://www.mdpi.com/2073-8994/9/12/297
work_keys_str_mv	AT linasong cohomologycharacterizationsofdiagonalnonabelianextensionsofregularhomliealgebras AT rongtang cohomologycharacterizationsofdiagonalnonabelianextensionsofregularhomliealgebras
_version_	1725825901927596032

Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras

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