| Issue |
Emergent Scientist
Volume 3, 2019
|
|
|---|---|---|
| Article Number | 4 | |
| Number of page(s) | 17 | |
| Section | Mathematics | |
| DOI | https://doi.org/10.1051/emsci/2019003 | |
| Published online | 04 June 2019 | |
Research Article
L∞-algebras and their cohomology
University of Göttingen Mathematical Institute, 37073 Göttingen, Germany
* e-mail: ben.reinhold@stud.uni-goettingen.de
Received:
29
January
2019
Accepted:
23
April
2019
We give an overview of different characterisations of L∞-structures in terms of symmetric brackets and (co)differentials on the symmetric (co)algebra. We then do the same for their representations (up to homotopy) and approach L∞-algebra cohomology using the commutator bracket on the space of coderivations of the symmetric coalgebra. This leads to abelian extensions of L∞-algebras by 2-cocycles.
Key words: L∞-algebras / representations (up to homotopy) / L∞-algebra cohomology / abelian extensions by 2-cocycles
© B. Reinhold, published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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