An $${\mathcal{A}_\infty}$$ A ∞ Operad in Spineless Cacti
نویسندگان
چکیده
منابع مشابه
On Spineless Cacti, Deligne’s Conjecture and Connes–kreimer’s Hopf Algebra
We give a new direct proof of Deligne’s conjecture on the Hochschild cohomology. For this we use the cellular chain operad of normalized spineless cacti as a model for the chains of the little discs operad. Previously, we had shown that the operad of spineless cacti is homotopy equivalent to the little discs operad. Moreover, we also showed that the quasi–operad of normalized spineless cacti is...
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We generalize our results on Deligne’s conjecture to prove the statement that the normalized Hochschild co–chains of a finite–dimensional associative algebra with a non–degenerate, symmetric, invariant inner product are an algebra over a chain model of the framed little discs operad which is given by cacti. In particular, in characteristic zero they are a BV algebra up to homotopy and the Hochs...
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We consider four operads which are different varieties of the cacti operad. These are cacti without local zeros (or spines) and cacti proper as well as both varieties with fixed constant size one of the constituting loops. We show that both types of cacti are a semi–direct products as operads of their normalized versions with a re–scaling operad based on R>0 which are homotopic to direct produc...
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1. Introduction. The purpose of this paper is to construct an operad J ^ with the good properties of both the little convex bodies partial operad Jf^ and the little cubes operad # " used in May's theory of E K ring spaces or multiplicative infinite loop spaces ((6), chapter VII). In (6) J^, can then be used instead of CriT^ and #< " , and the theory becomes much simpler; in particular all parti...
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A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by generators and relations which have some similarity with the Arnold relations for the cohomology of the type A hyperplane arrangement. A map from the operad Ram to t...
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ژورنال
عنوان ژورنال: Mediterranean Journal of Mathematics
سال: 2015
ISSN: 1660-5446,1660-5454
DOI: 10.1007/s00009-015-0577-4