Speaker
Description
Let $I$ be an ideal in some commutative (associative) algebra $O$. Starting from 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 a beautiful structure of a forest of decorated trees and is related to an $A_\infty$ 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 Laurent-Gengoux.
