On the perturbation algebra
Chuang, J. & Lazarev, A. (2018). On the perturbation algebra. Journal of Algebra, 519, pp. 130-148. doi: 10.1016/j.jalgebra.2018.10.032
Abstract
We introduce a certain differential graded bialgebra, neither commutative nor cocommutative, that governs perturbations of a differential on complexes supplied with an abstract Hodge decomposition. This leads to a conceptual treatment of the Homological Perturbation Lemma and its multiplicative version. As an application we give an explicit form of the decomposition theorem for A∞ algebras and A∞ modules and, more generally, for twisted objects in differential graded categories.
| Publication Type: | Article |
|---|---|
| Additional Information: | © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Publisher Keywords: | Abstract Hodge decomposition, differential graded algebra, Maurer-Cartan element |
| Subjects: | Q Science > QA Mathematics |
| Departments: | School of Science & Technology > Mathematics |
| SWORD Depositor: |
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