Polyadization of algebraic structures
Abstract
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.
Cite
@article{arxiv.2208.04695,
title = {Polyadization of algebraic structures},
author = {Steven Duplij},
journal= {arXiv preprint arXiv:2208.04695},
year = {2022}
}
Comments
21 pages, amslatex, bibliography updated, the second kind of the double decomposition (3.24) is added, Example 3.12 and Remark 3.13 are added