Homotopy derivations
Algebraic Topology
2015-10-02 v2 K-Theory and Homology
Abstract
We define a strong homotopy derivation of (cohomological) degree k of a strong homotopy algebra over an operad P. This involves resolving the operad obtained from P by adding a generator with "derivation relations". For a wide class of Koszul operads P, in particular Ass and Lie, we describe the strong homotopy derivations by coderivations and show that they are closed under the Lie bracket. We show that symmetrization of a strong homotopy derivation of an A-infinity algebra yields a strong homotopy derivation of the symmetrized L-infinity algebra. We give examples of strong homotopy derivations generalizing inner derivations.
Cite
@article{arxiv.1409.1691,
title = {Homotopy derivations},
author = {Martin Doubek and Tom Lada},
journal= {arXiv preprint arXiv:1409.1691},
year = {2015}
}
Comments
29 pages, v2: added full proof of Theorem 2.5, added Appendix 6.2 on coderivations, some other minor changes