Pinczon Algebras
Quantum Algebra
2012-11-13 v1
Abstract
After recalling the construction of a graded Lie bracket on the space of cyclic multilinear forms on a vector space V, due to Georges Pinczon and Rosane Ushirobira, we prove this construction gives a structure of quadratic associative algebra, up to homotopy, on V. In the associative case, it is easy to refind the associated usual Hochshild cohomology. By considering restriction to a subspace or a quotient space of forms, we can present in a completely similar way the cases of quadratic commutative and quadratic Lie algebras, up to homotopy, and the corresponding Harrison and Chevalley cohomologies.
Cite
@article{arxiv.1211.2611,
title = {Pinczon Algebras},
author = {Didier Arnal},
journal= {arXiv preprint arXiv:1211.2611},
year = {2012}
}