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Particle-like, dyx-coaxial and trix-coaxial Lie algebra structures for a multi-dimensional continuous Toda type system
Nuclear Physics B ( IF 2.5 ) Pub Date : 2020-09-22 , DOI: 10.1016/j.nuclphysb.2020.115187
Marcella Palese , Ekkehart Winterroth

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.



中文翻译:

多维连续Toda型系统的类粒子,dyx同轴和Trix同轴Lie代数结构

我们用 2+1个维Toda型系统是相关的代数骨架,它们是dyons和triadons型粒子状Lie代数的(兼容组合)。我们从系统的某些特定选择的代数骨架中获得与系统相关的Trix同轴和dyx同轴Lie代数结构,以兼容相关的绝对平行度。特别是,通过绝对并行性的第一选择,我们将与2+1个三维Toda型系统是一个三同轴同轴Lie代数结构,由两个(相容的)基本三单元组构成2-catena。此外,通过绝对平行度的第二种选择,我们关联了由两个(兼容)基本达因构成的dyx同轴Lie代数结构,以及由单个3达因构成的类粒子Lie代数结构。给出了一些明确的应用示例,例如与特殊解有关的守恒律和反谱问题。

更新日期:2020-09-29
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