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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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 |