Rota-Baxter family $\Omega$-associative conformal algebras and their cohomology theory

Abstract

In this paper, we first propose the concept of Rota-Baxter family $\Omega$-associative conformal algebras, then we study the cohomology theory of Rota-Baxter family $\Omega$-associative conformal algebras of any weight and justify it by interpreting the lower degree cohomology groups as formal deformations.

33pages. Some notations have been revised. arXiv admin note: text overlap with arXiv:2108.06744, arXiv:2204.13518, arXiv:2204.00160 by other authors