A cohomological study of modified Rota-Baxter algebras
Abstract
A modified Rota-Baxter algebra is an algebra equipped with an operator that satisfies the modified Yang-Baxter equation. In this paper, we define the cohomology of a modified Rota-Baxter algebra with coefficients in a suitable bimodule. We relate our cohomology of a modified Rota-Baxter algebra with the known cohomology theory of a Rota-Baxter algebra. As applications of our cohomology, we study formal one-parameter deformations and abelian extensions of modified Rota-Baxter algebras.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.