TY - JOUR
AU - Duplij, Steven
AB - Abstract: A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in the block-diagonal matrix form (Wedderburn decomposition), a general form of polyadic structures is given by block-shift matrices. We combine these forms in a special way to get a general shape of semisimple nonderived polyadic structures. 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.
TI - Polyadization of algebraic structures
JF - High Energy Physics - Theory
DO - 10.48550/arXiv.2208.04695
DA - 2022-07-29
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/polyadization-of-algebraic-structures-FOGx0PdKXE
VL - 2022
IS - 2208
DP - DeepDyve
ER -