Algebraic & Geometric Topology

On a Hopf operad containing the Poisson operad

Frédéric Chapoton

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Abstract

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 the dual operad of R is defined which we conjecture to be a isomorphism.

Article information

Source
Algebr. Geom. Topol., Volume 3, Number 2 (2003), 1257-1273.

Dates
Received: 20 January 2003
Revised: 12 December 2003
Accepted: 18 December 2003
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882435

Digital Object Identifier
doi:10.2140/agt.2003.3.1257

Mathematical Reviews number (MathSciNet)
MR2026333

Zentralblatt MATH identifier
1059.18005

Subjects
Primary: 18D50: Operads [See also 55P48]
Secondary: 16W30

Keywords
Hopf operad coalgebra chain complex

Citation

Chapoton, Frédéric. On a Hopf operad containing the Poisson operad. Algebr. Geom. Topol. 3 (2003), no. 2, 1257--1273. doi:10.2140/agt.2003.3.1257. https://projecteuclid.org/euclid.agt/1513882435


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References

  • V I Arnold, The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227–231
  • F Chapoton, A Hopf operad of forests of binary trees and related finite-dimensional algebras. (Sept. 2002).
  • W Y C Chen, V J W Guo, Bijections behind the Ramanujan polynomials, Adv. in Appl. Math. 27 (2001) 336–356, special issue in honor of Dominique Foata's 65th birthday (Philadelphia, PA, 2000)
  • F R Cohen, The homology of ${C}_{n+1}$-spaces, $n\geq 0$, from: “The homology of iterated loop spaces.”, Lecture Notes in Mathematics 533, Springer (1976)
  • F R Cohen, Artin's braid groups, classical homotopy theory, and sundry other curiosities, from: “Braids (Santa Cruz, CA, 1986)”, Contemp. Math. 78, Amer. Math. Soc., Providence, RI (1988) 167–206
  • S Fomin, A N Kirillov, Quadratic algebras, Dunkl elements, and Schubert calculus, from: “Advances in geometry”, Progr. Math. 172, Birkhäuser Boston, Boston, MA (1999) 147–182
  • M Gerstenhaber, A A Voronov, Homotopy $G$-algebras and moduli space operad, Internat. Math. Res. Notices (1995) 141–153 (electronic)
  • M Markl, Distributive laws and Koszulness, Ann. Inst. Fourier (Grenoble) 46 (1996) 307–323
  • O Mathieu, The symplectic operad, from: “Functional analysis on the eve of the 21st century, Vol. 1 (New Brunswick, NJ, 1993)”, Progr. Math. 131, Birkhäuser Boston, Boston, MA (1995) 223–243
  • A Varchenko, I Gelfand, Heaviside functions of a configuration of hyperplanes, Funktsional. Anal. i Prilozhen. 21 (1987) 1–18, 96
  • A A Voronov, The Swiss-cheese operad, from: “Homotopy invariant algebraic structures (Baltimore, MD, 1998)”, Contemp. Math. 239, Amer. Math. Soc., Providence, RI (1999) 365–373