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Curved Koszul duality of algebras over unital versions of binary operads. (English) Zbl 07595193

Summary: 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.

MSC:

18M70 Algebraic operads, cooperads, and Koszul duality
16S37 Quadratic and Koszul algebras
18G10 Resolutions; derived functors (category-theoretic aspects)
17B63 Poisson algebras
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