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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-12-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/9/12/297 |
| Summary: | 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. |
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| ISSN: | 2073-8994 |