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arXiv · 1603.00435

Quadratic and pinczon algebras

Didier Arnal·Wissem Bakbrahem·Mohamed Selmi
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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.

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Didier Arnal, Wissem Bakbrahem, Mohamed Selmi. 2016-03-01. Quadratic and pinczon algebras. https://arxiv.org/abs/1603.00435

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