Skip to main content
SpringerLink
Log in

Grothendieck–Teichmüller and Batalin–Vilkovisky

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

It is proven that, for any affine supermanifold M equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck–Teichmüller Lie algebra \({\mathfrak{grt}_1}\) on the set of quantum BV structures (i.e. solutions of the quantum master equation) on M.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Campos, R., Merkulov, S., Willwacher, T.: The Frobenius properad is Koszul (preprint arXiv:1402.4048)

  2. Dolgushev V.: Covariant and equivariant formality theorems. Adv. Math. 191(1), 147–177 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Drinfeld V.: On quasitriangular quasi-Hopf algebras and a group closely connected with \({Gal(\bar{Q}/Q)}\). Leningrad Math. J. 2(4), 829–860 (1991)

    MathSciNet  Google Scholar 

  4. Gerstenhaber M., Voronov A.A.: Homotopy G-algebras and moduli space operad. IMRN 3, 141–153 (1995)

    Article  MathSciNet  Google Scholar 

  5. Kapranov M., Manin Yu.I.: Modules and Morita theorem for operads. Am. J. Math. 123(5), 811–838 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Khudaverdian H.: Semidensities on odd symplectic supermanifolds. Commun. Math. Phys. 247, 353–390 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. Kontsevich, M.: Formality conjecture. In: Sternheimer, D., et al. (eds.) Deformation Theory and Symplectic Geometry, pp. 139–156. Kluwer, Dordrecht (1997)

  8. Kontsevich M.: Deformation quantization of Poisson manifolds. Lett. Math. Phys. 66, 157–216 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. Kravchenko, O.: Deformations of Batalin–Vilkovisky algebras. In: Poisson Geometry (Warsaw, 1998), Banach Center Publ., vol. 51, pp. 131–139. Polish Acad. Sci., Warsaw (2000)

  10. Loday J.-L., Vallette B.: Algebraic Operads. Number 346 in Grundlehren der mathematischen Wissenschaften. Springer, Berlin (2012)

    Google Scholar 

  11. Schwarz A.: Geometry of Batalin–Vilkovisky quantization. Commun. Math. Phys. 155, 249–260 (1993)

    Article  ADS  MATH  Google Scholar 

  12. Tamarkin, D.: Action of the Grothendieck–Teichmüller group on the operad of Gerstenhaber algebras (preprint arXiv:math/0202039)

  13. Willwacher, T.: M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra (preprint arXiv:1009.1654)

Download references

Author information

Author notes

  1. Sergei Merkulov

    Present address: Mathematics Research Unit, University of Luxembourg, Walferdange, Grand Duchy of Luxembourg

Authors and Affiliations

  1. Department of Mathematics, Stockholm University, 10691, Stockholm, Sweden

    Sergei Merkulov

  2. Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Thomas Willwacher

Authors
  1. Sergei Merkulov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Willwacher
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Willwacher.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Merkulov, S., Willwacher, T. Grothendieck–Teichmüller and Batalin–Vilkovisky. Lett Math Phys 104, 625–634 (2014). https://doi.org/10.1007/s11005-014-0692-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-014-0692-3

Mathematics Subject Classification (1991)

Keywords

Search

Navigation