April 17, 2023 to July 14, 2023
Institut Henri Poincaré, Paris
Europe/Paris timezone

Thomas Strobl : Arborescent Koszul-Tate resolutions and BFV for singular coisotropic reductions

Jul 4, 2023, 8:45 AM
Amphi Hermite

Amphi Hermite


Let I be an ideal in a commutative (associative) algebra O. Starting
from a resolution of O/I as an O-module, we construct a Koszul-Tate
resolution for this quotient, i.e.\ a graded symmetric algebra over O
with a differential which provides simultaneously a resolution as an
O-module. This algebra resolution has the beautiful structure of a
forest of decorated trees and is related to an A-infinity algebra on the
original module resolution. 

Considering O to be a Poisson algebra
and I a finitely generated Poisson subalgebra, we use the above
construction to obtain the corresponding BFV formulation. Its cohomology
at degree zero is proven to coincide with the reduced Poisson algebra
N(I)/I, where N(I) is the normaliser of I inside O, thus
generalising ordinary coisotropic reduction to the singular setting. As
an illustration we use the example where O consists of functions on
T^*(\R^3) and I is the ideal generated by angular momenta. 

This is joint work with Aliaksandr Hancharuk and, in part, with Camille

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