Bimodules

A bimodule is a mathematical structure that acts as a bridge between two algebraic systems, called algebras. Specifically, it is a set equipped with compatible actions from both algebras—one acting on the left and the other on the right—such that these actions interact coherently. This allows the bimodule to serve as a conduit for translating information and relationships between the two algebras. Bimodules are important in areas like algebra and representation theory because they help understand how different algebraic systems relate, combine, or transform into each other.