Higher Braid Groups and Regular Semigroups from Polyadic-Binary Correspondence

In this note, we first consider a ternary matrix group related to the von Neumann regular semigroups and Artin braid (in an algebraic way). The product of special kind matrices (idempotent finite order) reproduces groups with their binary multiplication components. We then generalize construction higher arity case, which allows us obtain some degree versions our sense) groups. latter are connected generalized polyadic equation R-matrix introduced by author, differ from any version well-known tetrahedron higher-dimensional analogs Yang-Baxter equation, n-simplex equations. Coxeter symmetry defined, it is shown that these only in non-higher case.