Koszul duality of En-operads
نویسندگان
چکیده
منابع مشابه
Koszul Duality of En-Operads
The goal of this paper is to prove a Koszul duality result for En-operads in differential graded modules over a ring. The case of an E1-operad, which is equivalent to the associative operad, is classical. For n > 1, the homology of an En-operad is identified with the n-Gerstenhaber operad and forms another well known Koszul operad. Our main theorem asserts that an operadic cobar construction on...
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The idea defining an operad goes back in a sense to Galois for which “the operations are mathematical objects”. This notion is used to model the operations acting on algebraic structures. For instance, there is an operad encoding associative algebras, Lie algebras and commutative algebras respectively. The definition of operad was first given in algebraic topology around 1970, where it was used...
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We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex K̄(r) formed by chains of partitions which starts at the smallest element and ends at the largest element of the partition poset. A classical theorem asserts that K̄(r) is equivalent to a wedge of r− 1-dimensional spheres. In addition, the poset of partitions is equipped with a natural action...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2010
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-010-0047-6