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Koszul duality of operads and homology of partition posets
Koszul duality operads homology partition posets
2015/3/25
We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex Kˉ(r) formed by chains of partitions which starts at the smallest element and ends at the larg...
Koszul duality for Operads
Koszul duality Operads
2015/3/25
This is a copy of the article by the same authors published in Duke Math. J. (1994).
A Koszul duality for props
Koszul duality props
2015/3/25
The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszu...
Manin products, Koszul duality, Loday algebras and Deligne conjecture
Manin products Koszul duality Loday algebras Deligne conjecture
2015/3/25
In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric o...
Koszul duality of affine Kac-Moody algebras and cyclotomic rational DAHA
Koszul duality affine Kac-Moody algebras cyclotomic rational DAHA
2011/8/22
Abstract: We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensional affin...
In this paper we prove a version of curved Koszul duality for Z/2Zgraded curved (dg) (co)algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool fo...