Intrinsic brackets and the $L_\infty$-deformation theory of bialgebras
Algebraic Topology
2010-05-24 v7 K-Theory and Homology
Abstract
We show that there exists a Lie a bracket on the cohomology of any type of (bi)algebras over an operad or a PROP, induced by a strongly homotopy Lie structure on the defining cochain complex, such that the associated "quantum" master equation captures deformations. This in particular implies the existence of a Lie bracket on the Gerstenhaber-Schack cohomology of a bialgebra that extends the classical intrinsic bracket on the Hochschild cohomology, giving an affirmative answer to an old question about the existence of such a bracket.
Keywords
Cite
@article{arxiv.math/0411456,
title = {Intrinsic brackets and the $L_\infty$-deformation theory of bialgebras},
author = {Martin Markl},
journal= {arXiv preprint arXiv:math/0411456},
year = {2010}
}
Comments
The final version. To appear in Journal of Homotopy and Related Structures