2025/06/04 by Qin, Yufei, Wang, Kai
#14A22 #16E45 #17B38 #17B63 #18N70 #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2506.03952
In this paper, we investigate pre-Calabi-Yau algebras and homotopy double Poisson algebras arising from homotopy Rota-Baxter structures. We introduce the notion of cyclic homotopy Rota-Baxter algebras, a class of homotopy Rota-Baxter algebras endowed with additional cyclic symmetry, and present a construction of such structures via a process called cyclic completion. We further introduce the concept of interactive pairs, consisting of two differential graded algebras-designated as the acting algebra and the base algebra-interacting through compatible module structures. We prove that if the acting algebra carries a suitable cyclic homotopy Rota-Baxter structure, then the base algebra inherits a natural pre-Calabi-Yau structure. Using the correspondence established by Fernandez and Herscovich between pre-Calabi-Yau algebras and homotopy double Poisson algebras, we describe the resulting homotopy Poisson structure on the base algebra in terms of homotopy Rota-Baxter algebra structure. In particular, we show that a module over an ultracyclic (resp. cyclic) homotopy Rota-Baxter algebra admits a (resp. cyclic) homotopy double Lie algebra structure.