  A generalization of the semisimplicity concept for polyadic algebraic
structures is proposed. If semisimple structures can be presented in block
diagonal matrix form (resulting in the Wedderburn decomposition), a general
form of polyadic structures is given by block-shift matrices. We combine these
forms to get a general shape of semisimple nonderived polyadic structures
("double" decomposition of two kinds). We then introduce the polyadization
concept (a "polyadic constructor") according to which one can construct a
nonderived polyadic algebraic structure of any arity from a given binary
structure. The polyadization of supersymmetric structures is also discussed.
The "deformation" by shifts of operations on the direct power of binary
structures is defined and used to obtain a nonderived polyadic multiplication.
Illustrative concrete examples for the new constructions are given.
