Curved Koszul duality of algebras over unital versions of binary operads

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.

Final version, to appear in J. Pure. Appl. Algebra

References in corpus (10)

• Nonhomogeneous quadratic duality and curvature
• Koszul duality of operads and homology of partition posets
• Higher enveloping algebras
• Homotopy unital A_infinity-algebras
• The Lambrechts-Stanley Model of Configuration Spaces
• Koszul duality and homotopy theory of curved Lie algebras
• Weyl n-algebras
• Homotopy theory of unital algebras
• Curved operadic calculus
• Algebraic operads up to homotopy

Cited by in corpus (1)

• Curved Koszul duality and cyclic (co)homology