Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Koszuality of the $\mathcal V^{(d)}$ dioperad   Define a $\mathcal V^{(d)}$-algebra as an associative algebra with a
symmetric and invariant co-inner product of degree $d$. Here, we consider
$\mathcal V^{(d)}$ as a dioperad which includes operations with zero inputs. We
show that the quadratic dual of $\mathcal V^{(d)}$ is $(\mathcal
V^{(d)})^!=\mathcal V^{(-d)}$ and prove that $\mathcal V^{(d)}$ is Koszul. We
also show that the corresponding properad is not Koszul contractible.

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The categories of this paper are: eess
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The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc