Operadic Gröbner Bases: An Implementation

  • Vladimir Dotsenko
  • Mikael Vejdemo-Johansson
Conference paper

DOI: 10.1007/978-3-642-15582-6_42

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)
Cite this paper as:
Dotsenko V., Vejdemo-Johansson M. (2010) Operadic Gröbner Bases: An Implementation. In: Fukuda K., Hoeven J..., Joswig M., Takayama N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg

Abstract

In an upcoming paper [1], the first author and Anton Khoroshkin define the concept of a Gröbner basis for finitely presented operads, prove the diamond lemma for these Gröbner bases, and demonstrate that having a quadratic Gröbner basis is equivalent to the existence of a Poincaré-Birkhoff-Witt basis. As demonstrated by Eric Hoffbeck [2], an operad with a PBW basis is Koszul. Thus, out of this emerges an entirely computational framework for proving Koszulness, as well as the possibility to build tools for exploration of operads by means of explicit calculation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Vladimir Dotsenko
    • 1
  • Mikael Vejdemo-Johansson
    • 2
  1. 1.Dublin Institute for Advanced Studies and School of MathematicsTrinity CollegeDublinIreland
  2. 2.Department of MathematicsStanford University 

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