Coloured Koszul duality and strongly homotopy operads

By P. V. D. Laan. 2003

50 citations recorded by the source corpus.

This paper proves Koszul duality for coloured operads and uses it to introduce strongly homotopy operads as a suitable homotopy invariant version of operads. It shows that rational chains on configuration spaces of points in the plane form a strongly homotopy operad quasi isomorphic to the chains on the little disks operad.

Subfields: Algebra and Number Theory, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/11680ff75829fc3bb51189004b823969918b24c9

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In Algebra and Number Theory

In Mathematical Physics

In Molecular Biology

Citations in the corpus

Curved Koszul duality theory (2010, methodology): “Following the ideas of van der Laan in [van03], we can extend this curved Koszul duality to coloured properads.”
Gröbner bases for operads (2008, background): “n polynomials can be deﬁned recursively as follows: ψ1 = 1, ψn+1 = ψn +(x + y)(nψn +x∂xψn). 5. Furtherdirections Ourresultscanbegeneralisedtothecaseofdioperads[11], 1 2PROPs[23], and coloured operads [32] in a rather straightforward way. For example, the dioperad of Lie bialgebras has a quadratic Gr”
Homotopy Algebras Inspired by Classical Open-Closed String Field Theory (2004, background): “The same fact holds true also for (weak) A∞-algebras, as explained in subsection 2.4 in [31] (the explicit form of the deformed A∞-structures can be found in [10, 11]).”
TRANSFERRING A^ (STRONGLY HOMOTOPY ASSOCIATIVE) STRUCTURES (2006, background): “A surprising interpretation of the p-kernel in terms of homotopy operads is suggested by [3].”