Formal Symplectic Realizations

Autor(es)

Cabrera, Alejandro ; Dherin, Benoit

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. 2016, n. 7, p. 26-pg., 2016-01-01.

Resumo

We study the relationship between several constructions of symplectic realizations of a given Poisson manifold. Our main result is a general formula for a formal symplectic realization in the case of an arbitrary Poisson structure on R-n. This formula is expressed in terms of rooted trees and elementary differentials, building on the work of Butcher, and the coefficients are shown to be a generalization of Bernoulli numbers appearing in the linear Poisson case. We also show that this realization coincides with a formal version of the original construction of Weinstein, when suitably put in global Darboux form, and with the realization coming from tree-level part of Kontsevich's star product. We provide a simple iterated integral expression for the relevant coefficients and show that they coincide with underlying Kontsevich weights. (AU)

• Processo FAPESP: 10/19365-0 - Geometrias monoidais
• Beneficiário: Benoit Richard Umbert Dherin
• Modalidade de apoio: Bolsas no Brasil - Jovens Pesquisadores
• Processo FAPESP: 10/15069-8 - Geometrias monoidais
• Beneficiário: Benoit Richard Umbert Dherin
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores