2022/03/06 by Kai Wang, Wang, Kai, Guodong Zhou +1 · 1 citation
Mathematics · #16E40 #17B38 #18M70 #Advanced Topics in Algebra #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2203.02960
openalex publication_date 2022/03/06 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
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_∞-algebra structure over it are exhibited as well.