Deformations and Cohomology Theory of Rota-Baxter Systems

Abstract

Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of Rota-Baxter systems. A further study on an $L_{\infty }$-algebra structure associated to this cohomology theory will be given in a subsequent paper.

26 pages. arXiv admin note: substantial text overlap with arXiv:2108.06744