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

Markl, 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 -