On quantizable odd Lie bialgebras

TL;DR

This paper introduces quantizable odd Lie bialgebras motivated by deformation quantization issues in infinite-dimensional Poisson structures, providing a minimal resolution of their governing properad and linking to quantizable Poisson structures.

Contribution

It constructs a minimal resolution of the properad for quantizable odd Lie bialgebras, advancing understanding of their algebraic structure and connection to quantizable Poisson structures.

Findings

Constructed a minimal resolution of the properad for quantizable odd Lie bialgebras

Linked the algebraic structures to quantizable Poisson structures

Provided new tools for deformation quantization in infinite dimensions

Abstract

Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so called quantizable Poisson structures.