Operads for n-ary algebras - calculations and conjectures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00372809" target="_blank" >RIV/67985840:_____/11:00372809 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Operads for n-ary algebras - calculations and conjectures

Original language description

We studied Koszulity of a family ${t/mathcal{A}/it ss}^n_d$ of operads depending on a natural number $n /in /mathbb{N}$ and on the degree $d /in /mathbb{Z}$ of the generating operation. While we proved that, for $n /le 7$, the operad ${t/mathcal{A}/it ss}^n_d$ is Koszul if and only if $d$ is even, and while it follows from [4] that ${t/mathcal{A}/it ss}^n_d$ is Koszul for $d$ even and arbitrary $n$, the (non)Koszulity of ${t/mathcal{A}/it ss}^n_d$ for $d$ odd and $n /ge 8$ remains an open problem. In this note we describe some related numerical experiments, and formulate a conjecture suggested by the results of these computations.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F08%2F0397" target="_blank" >GA201/08/0397: Algebraic methods in geometry and topology</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Archivum mathematicum

ISSN

0044-8753

e-ISSN

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Volume of the periodical

47

Issue of the periodical within the volume

5

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

11

Pages from-to

377-387

UT code for WoS article

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EID of the result in the Scopus database

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