Rota-Baxter modules toward derived functors

Abstract

In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and resulting difference between Rota-Baxter modules and the usual modules over an algebra. We introduce the concepts of free, projective, injective and flat Rota-Baxter modules. We give the construction of free modules and show that there are enough projective, injective and flat Rota-Baxter modules to provide the corresponding resolutions for derived functor.

21 pages

References in corpus (3)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• A Unified Algebraic Approach to Classical Yang-Baxter Equation
• Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion

Cited by in corpus (1)

• Representations and cohomologies of relative Rota-Baxter Lie algebras and applications