Cayley Hash Values of Brauer Messages and Some of Their Applications in the Solutions of Systems of Differential Equations

Cayley hash values are defined by paths of some oriented graphs (quivers) called graphs, whose vertices and arrows given elements a group H. On the other hand, Brauer messages obtained concatenating words associated with multisets constituting configurations configurations. These define named quivers which induce particular class bound quiver algebras configuration algebras. Elements in can be seen as letters messages. This paper proves that each point (x,y)∈V=R\{0}×R\{0} has an algebra ΛB(x,y) induced B(x,y). Additionally, points subset form (⌊(x)⌋,⌈(x)⌉]×(⌊(y)⌋,⌈(y)⌉]⊂V have same dimension. We give analysis M(B(x,y)) semigroup generated appropriated matrices A0,A1,A2∈GL(2,R) over commutative ring R. As application, we use to construct explicit solutions for systems linear nonlinear differential equations X″(t)+MX(t)=0 X′(t)−X2(t)N(t)=N(t) suitable square matrices, M N(t). Python routines compute also included.