Quadratic and pinczon algebras
Quantum Algebra
2016-08-08 v1
Abstract
Given a symmetric non degenerated bilinear form b on a vector space V, G. Pinczon and R. Ushirobira defined a bracket {,} on the space of multilinear skewsymmetric forms on V. With this bracket, the quadratic Lie algebra structure equation on (V, b) becomes simply {\^a, \^a} = 0. We characterize similarly quadratic associative, commutative or pre-Lie structures on (V, b) by the same equation {\^a, \^a} = 0, but on different spaces of forms. These definitions extend to quadratic up to homotopy algebras and allows to describe the corresponding cohomologies.
Cite
@article{arxiv.1603.00435,
title = {Quadratic and pinczon algebras},
author = {Didier Arnal and Wissem Bakbrahem and Mohamed Selmi},
journal= {arXiv preprint arXiv:1603.00435},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1211.2611