Particle-like, dyx-coaxial and trix-coaxial Lie algebra structures for a multi-dimensional continuous Toda type system

• Published in: arXiv.org
• Main Authors: Palese, Marcella, Winterroth, Ekkehart
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 31.08.2020
• Subjects: Algebra; Compatibility; Lie groups; Mathematics - Mathematical Physics; Physics - Exactly Solvable and Integrable Systems; Physics - Mathematical Physics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2006.14227

We prove that with a \((2+1)\)-dimensional Toda type system are associated algebraic skeletons which are (compatible assemblings) of particle-like Lie algebras of dyons and triadons type. We obtain trix-coaxial and dyx-coaxial Lie algebra structures for the system from algebraic skeletons of some particular choice for compatible associated absolute parallelisms. In particular, by a first choice of the absolute parallelism, we associate with the \((2+1)\)-dimensional Toda type system a trix-coaxial Lie algebra structure made of two (compatible) base triadons constituting a \(2\)-catena. Furthermore, by a second choice of the absolute parallelism, we associate a dyx-coaxial Lie algebra structure made of two (compatible) base dyons, as well as particle-like Lie algebra structures made of single \(3\)-dyons. Some explicit examples of applications such as conservation laws related to special solutions, and an inverse spectral problem are worked out.