Discrete-time systems in quasi-standard form and the ${\mathfrak{h}}_6$ coalgebra symmetry

Abstract

In this paper, we characterize all discrete-time systems in quasi-standard form admitting coalgebra symmetry with respect to the Lie--Poisson algebra ${\mathfrak{h}}_6$. The outcome of this study is a family of systems depending on an arbitrary function of three variables, playing the rôle of the potential. Moreover, using a direct search approach, we classify discrete-time systems from this family that admit an additional invariant at most quadratic in the physical variables. We discuss the integrability properties of the obtained cases, their relationship with known systems, and their continuum limits.

arXiv comment34 pages, 2 tables

References in corpus (23)

• Classical and Quantum Superintegrability with Applications
• A systematic construction of completely integrable Hamiltonians from coalgebras
• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• A maximally superintegrable system on an n-dimensional space of nonconstant curvature
• An introduction to quantized Lie groups and algebras
• Maximal superintegrability of the generalized Kepler--Coulomb system on N-dimensional curved spaces
• (Super)integrability from coalgebra symmetry: formalism and applications
• Embedding of the Racah Algebra R($\mathbf{n}$) and Superintegrability
• Comodule algebras and integrable systems
• Classical and quantum higher order superintegrable systems from coalgebra symmetry
• Integrable four-dimensional symplectic maps of standard type
• Superintegrable systems with spin induced by coalgebra symmetry
• The Racah algebra: An overview and recent results
• Quantum Integrals from Coalgebra Structure
• Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
• Racah Algebra $R(n)$ from Coalgebraic Structures and Chains of $R(3)$ Substructures
• N-dimensional integrability from two-photon coalgebra symmetry
• The ${\mathfrak{sl}}_2(\mathbb{R})$ coalgebra symmetry and the superintegrable discrete-time systems
• Coalgebra symmetry for discrete systems
• On the inverse problem of the discrete calculus of variations
• Polynomial algebras from commutants: Classical and Quantum aspects of ${\mathcal{A}}_3$

Cited by in corpus (2)

• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Explicit isomorphisms for the symmetry algebras of continuous and discrete isotropic oscillators