Non-weight modules over generalized Heisenberg–Virasoro algebra of rank two

Puntos clave

• Each non-weight module is classified in relation to the Cartan subalgebra, highlighting their structural importance in representation theory.
• The irreducible L̃(p1,p2)-modules demonstrate intricate properties, establishing a basis for further algebraic exploration.
• This work engages with theoretical algebra by revealing properties of generalized Heisenberg-Virasoro algebras, indicating prospective applications in higher dimensional representations.
• Comprehensive classification of rank two modules prompts future studies on the interaction between algebraic structures and their representations.