| Title:
|
Extensions of hom-Lie algebras in terms of cohomology (English) |
| Author:
|
Armakan, Abdoreza R. |
| Author:
|
Farhangdoost, Mohammed Reza |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
317-328 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra $\frak {g}$ by another hom-Lie algebra $\frak {h}$ and discuss the case where $\frak {h}$ has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie algebras, i.e., we show that in order to have an extendible hom-Lie algebra, there should exist a trivial member of the third cohomology. (English) |
| Keyword:
|
hom-Lie algebras |
| Keyword:
|
cohomology of hom-Lie algebras |
| Keyword:
|
extensions of hom-Lie algebras |
| MSC:
|
17B99 |
| MSC:
|
55U15 |
| idZBL:
|
Zbl 06738521 |
| idMR:
|
MR3661043 |
| DOI:
|
10.21136/CMJ.2017.0576-15 |
| . |
| Date available:
|
2017-06-01T14:25:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146758 |
| . |
| Reference:
|
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