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Showing 1 to 5 of 5 for “"Koszul Duality"”.
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Koszul duality for multigraded algebras
Classical Koszul duality sets up an adjoint pair of functors establishing an equivalence of categories. The equivalence is between the bounded derived category of complexes of graded modules over a graded algebra and the bounded derived category of complexes of graded modules over the quadratic …
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Koszul duality and the bar spectral sequence
… for algebras over a spectral operad relates Koszul duality phenomena in several contexts. In this thesis, we apply this classical tool to the Koszul dual pair given by the (non-unital) E subscript ∞-operad and the spectral Lie operad over Fₚ. The bar spectral sequence for E subscript …
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2D Chiral Algebras from Koszul Duality & Associativity
… thesis, we will explain how the techniques of Koszul duality and associativity can be used to completely determine certain celestial chiral algebras, characterizing collinear splitting functions not just at tree-level but to arbitrary loop order. To apply this technique, and indeed for the …
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Tilting sheaves for real groups and Koszul duality
For a certain class of real analytic varieties with the real Lie group action we define a tstructure on the category of equivariant-monodromic sheaves and develop the theory of tilting sheaves. In case of a quasi-split real form of an algebraic group acting on the flag variety we construct an …
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The Koszul dual to n-Lie, n-Com algebras, and Young tableaux
… to more than one Hamiltonian. We find the Koszul dual of $n\text{-}Lie_{-d+n-2}$ to be the operad $n\text{-}Com_d$, whose relations come from the Specht module $S^{(n,n-1)}$. We combine the operads $n$-Lie and $m$-Com to construct the operad $(m,n)-Poiss$, where the rewriting rule that …