Comodule algebras and integrable systems

TL;DR

This paper introduces a method to construct classical and quantum integrable systems using comodule algebras, providing explicit models based on various algebraic structures.

Contribution

It presents a novel approach to generate integrable systems from (Jordan-Lie) comodule algebras, including explicit models with diverse algebraic frameworks.

Findings

Constructed integrable models based on so(2,1) comodule algebra

Developed models using non-standard Schrodinger comodule algebras

Created integrable systems from q-oscillator and Reflection Equation algebras

Abstract

A method to construct both classical and quantum completely integrable systems from (Jordan-Lie) comodule algebras is introduced. Several integrable models based on a so(2,1) comodule algebra, two non-standard Schrodinger comodule algebras, the (classical and quantum) q-oscillator algebra and the Reflection Equation algebra are explicitly obtained.