# Operads for $n$-ary algebras – calculations and conjectures

Archivum Mathematicum (2011)

- Volume: 047, Issue: 5, page 377-387
- ISSN: 0044-8753

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topMarkl, Martin, and Remm, Elisabeth. "Operads for $n$-ary algebras – calculations and conjectures." Archivum Mathematicum 047.5 (2011): 377-387. <http://eudml.org/doc/246928>.

@article{Markl2011,

abstract = {In [8] 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.},

author = {Markl, Martin, Remm, Elisabeth},

journal = {Archivum Mathematicum},

keywords = {operad; Koszulity; minimal model; operad; Koszulity; minimal model},

language = {eng},

number = {5},

pages = {377-387},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Operads for $n$-ary algebras – calculations and conjectures},

url = {http://eudml.org/doc/246928},

volume = {047},

year = {2011},

}

TY - JOUR

AU - Markl, Martin

AU - Remm, Elisabeth

TI - Operads for $n$-ary algebras – calculations and conjectures

JO - Archivum Mathematicum

PY - 2011

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 047

IS - 5

SP - 377

EP - 387

AB - In [8] 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.

LA - eng

KW - operad; Koszulity; minimal model; operad; Koszulity; minimal model

UR - http://eudml.org/doc/246928

ER -

## References

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- Markl, M., Intrinsic brackets and the ${L}_{\infty}$-deformation theory of bialgebras, J. Homotopy Relat. Struct. 5 (1) (2010), 177–212. (2010) MR2812919
- Markl, M., Remm, E., (Non–)Koszulness of operads for n-ary algebras, galgalim and other curiosities, Preprint arXiv:0907.1505.
- Markl, M., Shnider, S., Stasheff, J. D., Operads in Algebra, Topology and Physics, Math. Surveys Monogr., vol. 96, Amer. Math. Soc., Providence, RI, 2002. (2002) Zbl1017.18001MR1898414

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