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	American 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

Keywords

Coloured operads
Grobner bases
Lie-Rinnehart algebras

All Science Journal Classification (ASJC) codes

Applied Mathematics

Access to Document

10.1007/s10231-021-01114-5

Cite this

@article{213bffa5bbee4be0b4b71161f4cf2605,

title = "Gr{\"o}bner bases for coloured operads",

abstract = "In this work, we develop the machinery of Gr{\"o}bner 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 Gr{\"o}bner basis, we consider the seminal Lie-Rinehart operad whose algebras include pairs (functions, vector fields).",

keywords = "Coloured operads, Grobner bases, Lie-Rinnehart algebras",

author = "Vladislav Kharitonov and Anton Khoroshkin",

note = "Publisher Copyright: {\textcopyright} 2021, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

month = feb,

doi = "10.1007/s10231-021-01114-5",

language = "American English",

volume = "201",

pages = "203--241",

journal = "Annali di Matematica Pura ed Applicata",

issn = "0373-3114",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

T1 - Gröbner bases for coloured operads

AU - Kharitonov, Vladislav

AU - Khoroshkin, Anton

PY - 2022/2

Y1 - 2022/2

N2 - 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).

AB - 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).

KW - Coloured operads

KW - Grobner bases

KW - Lie-Rinnehart algebras

UR - http://www.scopus.com/inward/record.url?scp=85106739300&partnerID=8YFLogxK

U2 - 10.1007/s10231-021-01114-5

DO - 10.1007/s10231-021-01114-5

M3 - Article

SN - 0373-3114

VL - 201

SP - 203

EP - 241

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 1

ER -

Gröbner bases for coloured operads

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this