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.

我们用 $（2+\mathrm{1个}）$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$（2+\mathrm{1个}）$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。