Geodesic
Operads for $n$-ary algebras – calculations and conjectures
Archivum mathematicum, Tome 47 (2011) no. 5, pp. 377-387 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 18D50, 55P48
Keywords: operad; Koszulity; minimal model 
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     title = {Operads for $n$-ary algebras {\textendash} calculations and conjectures},
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Markl, Martin; Remm, Elisabeth. Operads for $n$-ary algebras – calculations and conjectures. Archivum mathematicum, Tome 47 (2011) no. 5, pp. 377-387. http://geodesic.mathdoc.fr/item/ARM_2011_47_5_a4/

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