Gröbner bases for coloured operads

Vladislav Kharitonov; Anton Khoroshkin

doi:10.1007/s10231-021-01114-5

Gröbner bases for coloured operads

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	203-241
Number of pages	39
Journal	Annali di Matematica Pura ed Applicata
Volume	201
Issue number	1
DOIs	https://doi.org/10.1007/s10231-021-01114-5
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

Access to Document

10.1007/s10231-021-01114-5

Cite this

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Gröbner bases for coloured operads

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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