Operadic Homological Algebra

  • Jean-Louis Loday
  • Bruno Vallette
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 346)

Abstract

The aim of this chapter is to develop homological algebra in the operadic context.

Keywords

Minimal Model Monoidal Category Homological Algebra Follow Diagram Commute Composite Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. BM03a.
    C. Berger and I. Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003), no. 4, 805–831. MathSciNetMATHCrossRefGoogle Scholar
  2. DCV11.
    G. Drummond-Cole and B. Vallette, Minimal model for the Batalin–Vilkovisky operad, ArXiv:1105.2008 (2011).
  3. Fre04.
    —, Koszul duality of operads and homology of partition posets, in “Homotopy theory and its applications (Evanston, 2002)”, Contemp. Math. 346 (2004), 115–215. MathSciNetCrossRefGoogle Scholar
  4. GJ94.
    E. Getzler and J. D. S. Jones, Operads, homotopy algebra and iterated integrals for double loop spaces, hep-th/9403055 (1994).
  5. GK94.
    V. Ginzburg and M. Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994), no. 1, 203–272. MathSciNetMATHCrossRefGoogle Scholar
  6. Kon99.
    —, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999), no. 1, 35–72, Moshé Flato (1937–1998). MathSciNetMATHCrossRefGoogle Scholar
  7. Kon03.
    —, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), no. 3, 157–216. MathSciNetMATHCrossRefGoogle Scholar
  8. Mar96b.
    —, Models for operads, Comm. Algebra 24 (1996), no. 4, 1471–1500. MathSciNetMATHCrossRefGoogle Scholar
  9. SV12.
    H. Strohmayer and B. Vallette, Homotopy theory of homotopy operads, Preprint (2012). Google Scholar
  10. Val07b.
    —, A Koszul duality for props, Trans. of Amer. Math. Soc. 359 (2007), 4865–4993. MathSciNetMATHCrossRefGoogle Scholar
  11. Wei94.
    C. A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 1994. MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jean-Louis Loday
    • 1
  • Bruno Vallette
    • 2
  1. 1.IRMA, CNRS et Université de StrasbourgStrasbourgFrance
  2. 2.Lab. de Mathématiques J.A. DieudonnéUniversité de Nice-Sophia AntipolisNiceFrance

Personalised recommendations