Pinczon Algebras

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [10 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00706402
Contributor : Didier Arnal <>
Submitted on : Monday, November 12, 2012 - 10:43:00 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Wednesday, February 13, 2013 - 3:43:37 AM

Files

PinczonAlgebras.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00706402, version 2
  • ARXIV : 1211.2611

Collections

Citation

Didier Arnal. Pinczon Algebras. 2012. ⟨hal-00706402v2⟩

Share

Metrics

Record views

182

Files downloads

109