Comodule algebras and integrable systems

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.

17 pages

References in corpus (9)

• Algebraic Structures Related to Reflection Equations
• A systematic construction of completely integrable Hamiltonians from coalgebras
• Integrable deformations of oscillator chains from quantum algebras
• Construction of completely integrable systems by Poisson mappings
• Quantum Groups, $q$-Oscillators and Covariant Algebras
• Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation
• Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
• The spin 1/2 Calogero-Gaudin System and its q-Deformation
• New time-type and space-type non-standard quantum algebras and discrete symmetries

Cited by in corpus (11)

• (Super)integrability from coalgebra symmetry: formalism and applications
• Integrable deformations of Rössler and Lorenz systems from Poisson-Lie groups
• Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
• Binary trees, coproducts, and integrable systems
• Coalgebra symmetry for discrete systems
• Superintegrable Deformations of the Smorodinsky-Winternitz Hamiltonian
• Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations
• Classification of real three-dimensional Poisson-Lie groups
• An integrable discretization of the rational su(2) Gaudin model and related systems
• Discrete-time systems in quasi-standard form and the ${\mathfrak{h}}_6$ coalgebra symmetry
• Universal coacting Poisson Hopf algebras