Curved Koszul duality of algebras over unital versions of binary operads

TL;DR

This paper develops a curved Koszul duality framework for unital binary operad algebras, providing explicit resolutions and applications to Poisson n-algebras, derived enveloping algebras, and factorization homology.

Contribution

It introduces a new curved Koszul duality theory for unital binary operad algebras and applies it to compute resolutions and invariants of Poisson n-algebras.

Findings

Explicit resolutions of Poisson n-algebras were computed.

Derived enveloping algebras were obtained using the new duality.

Factorization homology on manifolds was calculated with these resolutions.

Abstract

We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson $n$-algebras given by polynomial functions on a standard shifted symplectic space. We compute explicit resolutions of these algebras using curved Koszul duality. We use these resolutions to compute derived enveloping algebras and factorization homology on parallelized simply connected closed manifolds with coefficients in these Poisson $n$-algebras.