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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).
We study P-Hopf algebras with one coassociative cooperation over different operads P. For example, we consider the Loday-Ronco dendriform Hopf algebra and its isomorphisms with the noncommutative plan...
Operads, homotopy algebra and iterated integrals for double loop spaces
Operads homotopy algebra iterated integrals double loop spaces
2015/3/25
This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended ...
Open-string vertex algebras, tensor categories and operads
Open-string vertex algebras tensor categories operads
2015/3/25
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the n...
This paper is dedicated to the memory of Moshe Flato, and will appear in Lett. Math. Phys. 48 (1).It became clear during last 5-6 years that the algebraic world of associative algebras (abelian catego...
Deformations of algebras over operads and Deligne's conjecture
algebras over operads Deligne's conjecture
2015/3/25
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of...
We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bi...
Dendroidal sets offer a formalism for the study of 1-operads akin to the formalism of 1-categories by means of simplicial sets. We present here an account of the current state of the theory while plac...
Deformations of algebras over operads and Deligne's conjecture
Deformations algebras operads Deligne's conjecture
2010/11/1
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces o...