Koszuality of the \(\mathcal V^{(d)}\) dioperad

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2018-10-30 DOI:10.1007/s40062-018-0220-8

Kate Poirier, Thomas Tradler

引用次数: 1

Abstract

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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\(\mathcal V^{(d)}\) dioperad的Koszuality

将\(\mathcal V^{(d)}\) -代数定义为具有d次对称不变内积的关联代数。这里，我们将\(\mathcal V^{(d)}\)视为包含零输入操作的二操作数。证明了\(\mathcal V^{(d)}\)的二次对偶是\((\mathcal V^{(d)})^!=\mathcal V^{(-d)}\)，并证明了\(\mathcal V^{(d)}\)是Koszul。我们还证明了相应的性质不是Koszul可收缩的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.