| Title:
|
On the adjoint map of homotopy abelian DG-Lie algebras (English) |
| Author:
|
Iacono, Donatella |
| Author:
|
Manetti, Marco |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
7-15 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general. (English) |
| Keyword:
|
differential graded Lie algebras |
| Keyword:
|
adjoint map |
| Keyword:
|
cofibrant resolutions |
| MSC:
|
17B70 |
| MSC:
|
18G55 |
| idZBL:
|
Zbl 07088753 |
| idMR:
|
MR3939059 |
| DOI:
|
10.5817/AM2019-1-7 |
| . |
| Date available:
|
2019-03-23T12:18:14Z |
| Last updated:
|
2020-02-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147645 |
| . |
| Reference:
|
[1] Bandiera, R.: Nonabelian higher derived brackets.J. Pure Appl. Algebra 219 (2015), 3292–3313. MR 3320220, 10.1016/j.jpaa.2014.10.015 |
| Reference:
|
[2] Bandiera, R.: Homotopy abelian $L_\infty $ algebras and splitting property.Rend. Mat. Appl. 37 (2016), 105–122, http://www1.mat.uniroma1.it/ricerca/rendiconti/37_1-2_(2016)_105-122.html. MR 3622306 |
| Reference:
|
[3] Hinich, V.: Homological algebra of homotopy algebras.Comm. Algebra 25 (1997), 3291–3323. MR 1465117, 10.1080/00927879708826055 |
| Reference:
|
[4] Iacono, D.: On the abstract Bogomolov-Tian-Todorov theorem.Rend. Mat. Appl. 38 (2017), 175–198, http://www1.mat.uniroma1.it/ricerca/rendiconti/38_2_(2017)_175-198.html. MR 3762711 |
| Reference:
|
[6] Manetti, M.: On some formality criteria for DG-Lie algebras.J. Algebra 438 (2015), 90–118. MR 3353026, 10.1016/j.jalgebra.2015.04.029 |
| . |
