Curved Koszul duality of algebras over unital versions of binary operads |
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| Affiliation: | 1. University of Missouri-Columbia, Mathematics Department, Columbia, MO, USA;2. College of the Ozarks, Mathematics Department, Point Lookout, MO, USA;1. Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan;2. Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan;1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D.F. 04510, Mexico;2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D.F. 04510, Mexico;3. Université de Paris et Sorbonne Université, CNRS, IMJ-PRG, Bâtiment Sophie Germain, 5 rue Thomas Mann, 75205 Paris Cedex 13, France;1. Instituto de Ciência, Engenharia e Tecnologia (ICET) - Universidade Federal dos Vales do Jequitinhonha e Mucuri (UFVJM), Campus do Mucuri, Teófilo Otoni - MG, Brazil;2. Faculdade de Ciências Exatas e Tecnologia (FACET) - Universidade Federal da Grande Dourados (UFGD), Rodovia Dourados - Itahum, Km 12 - Cidade Universitátia, Dourados - MS, Brazil |
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| 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. |
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| Keywords: | 18M70 16S37 18G10 17B63 |
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