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 language | English |
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Pages (from-to) | 203-241 |
Number of pages | 39 |
Journal | Annali di Matematica Pura ed Applicata |
Volume | 201 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2022 |
Externally published | Yes |
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