论文标题
与任意重量的Rota-Baxter Operad的最小模型
The minimal model of Rota-Baxter operad with arbitrary weight
论文作者
论文摘要
本文调查了任意权重的rota-baxter联想代数，即从操作观点上赋予了与任意权重的rota-baxter运算符的联想代数。用$ \ rb $表示rota-baxter协会代数的出手。明确构建了同型库里德（Cooperad），可以看作是$ \ rb $的koszul双重二元组合，因为事实证明，这种同型库里德的cobar构造恰好是$ \ rb $的最小型号。这使我们能够给出同型rota-baxter联想代数的概念。也展示了Rota-baxter联想代数和基础$ L_ \ Infty $ -Algebra结构的变形复合物。
This paper investigates Rota-Baxter associative algebras of of arbitrary weights, that is, associative algebras endowed with Rota-Baxter operators of arbitrary weights from an operadic viewpoint. Denote by $\RB$ the operad of Rota-Baxter associative algebras. A homotopy cooperad is explicitly constructed, which can be seen as the Koszul dual of $\RB$ as it is proven that the cobar construction of this homotopy cooperad is exactly the minimal model of $\RB$. This enables us to give the notion of homotopy Rota-Baxter associative algebras. The deformation complex of a Rota-Baxter associative algebra and the underlying $L_\infty$-algebra structure over it are exhibited as well.
