Polyadic Systems and their Multiplace Representations

Polyadic Systems and their Multiplace representations

Ternary algebraic operations (with the arity n= 3 ) were introduced by A. Cayley in 1845 and later by J. J. Sylvester in 1883. The notion of an n -ary group was introduced in 1928 by D ¨ ORNTE [1929] (inspired by E. N¨other). The coset theorem of Post explained the connection between n -ary groups and their covering binary groups POST [1940]. The next step in study of n -ary groups was the Gluskin-Hossz ´u theorem HOSSZ´ U[1963], GLUSKIN[1965]. The cubic and n -ary generalizations of matrices and determinants were made in KAPRANOV ET AL. [1994], SOKOLOV [1972], physical application in KAWAMURA [2003], RAUSCH DE TRAUBENBERG[2008].

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