Curved Koszul duality of algebras over unital versions of binary operads

Najib Idrissi
J. Pure Appl. Algebra 227.3 (March 2023)
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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 nn-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 nn-algebras.