Gröbner bases for coloured operads

Vladislav Kharitonov, Anton Khoroshkin

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, we develop the machinery of Gröbner bases for coloured operads, which allows us to establish a useful criterion of Koszulness of a coloured operad. Among the examples for which we show the existence of a quadratic Gröbner basis, we consider the seminal Lie-Rinehart operad whose algebras include pairs (functions, vector fields).

Original languageEnglish
Pages (from-to)203-241
Number of pages39
JournalAnnali di Matematica Pura ed Applicata
Volume201
Issue number1
DOIs
StatePublished - Feb 2022
Externally publishedYes

Bibliographical note

Funding Information:
We would like to thank V. Dotsenko and P. Tamaroff for useful comments on the first draft of the text. The research of A.Kh. was carried out within the HSE University Basic Research Program and funded (jointly) by the Russian Academic Excellence Project ’5-100’. The results of Sect. have been obtained under support of the RSF Grant No.19-11-00275.

Funding Information:
We would like to thank V.?Dotsenko and P.?Tamaroff for useful comments on the first draft of the text. The research of A.Kh. was carried out within the HSE University Basic Research Program and funded (jointly) by the Russian Academic Excellence Project ?5-100?. The results of Sect.?3 have been obtained under support of the RSF Grant No.19-11-00275.

Publisher Copyright:
© 2021, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

  • Coloured operads
  • Grobner bases
  • Lie-Rinnehart algebras

ASJC Scopus subject areas

  • Applied Mathematics

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