Related papers: Polyadic supersymmetry
We introduce a new class of division algebras, the hyperpolyadic algebras, which correspond to the binary division algebras $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, $\mathbb{O}$ without considering new elements. First, we use the matrix…
We generalize $\sigma$-matrices to higher arities using the polyadization procedure proposed by the author. We build the nonderived $n$-ary version of $SU\left( 2\right) $ using cyclic shift block matrices. We define a new function, the…
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…
We generalize the Grothendieck construction of the completion group for a monoid (being the starting point of the algebraic $K$-theory) to the polyadic case, when an initial semigroup is $m$-ary and the corresponding final class group…
This paper introduces and systematically develops the theory of polyadic group rings, a higher arity generalization of classical group rings $\mathcal{R}[\mathsf{G}]$. We construct the fundamental operations of these structures, defining…
This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate…
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the…
Usually when we have polyadic-like algebras, meaning that we have infinitary substitutions (that is substitutions moving infinitely many points) in the similarity type, then we get the superamalgamation property especially if this class of…
Concrete two-set (module-like and algebra-like) algebraic structures are investigated from the viewpoint that the initial arities of all operations are arbitrary. Relations between operations arising from the structure definitions, however,…
Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic…
We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: the arity of the product can differ from that of the constituents, and the elements from…
We report a new type of supersymmetry, "N-fold supersymmetry", in one-dimensional quantum mechanics. Its supercharges are N-th order polynomials of momentum: It reduces to ordinary supersymmetry for N=1, but for other values of N the…
We construct positional numeral systems that work natively over nonderived polyadic $\left( m,n\right) $-rings whose addition takes $m$ arguments and multiplication takes $n$. In such rings, the length of an admissible additive word and a…
We consider a Pauli particle in a Coulomb field. The supersymmetric Hamiltonian is constructed, by explicitly giving the two supercharges $Q_{1}$ and $ Q_{2}$ in the full three-dimensional space and which together with the Hamiltonian, are…
This article continues the study of concrete algebra-like structures in our polyadic approach, where the arities of all operations are initially taken as arbitrary, but the relations between them, the arity shapes, are to be found from some…
We describe how the usual supercharges of extended supersymmetry may be {\it twisted} to produce a BRST-like supercharge $Q$. The usual supersymmetry algebra is then replaced by a twisted algebra and the action of the twisted theory is…
The polyadic integer numbers, which form a polyadic ring, are representatives of a fixed congruence class. The basics of polyadic arithmetic are presented: prime polyadic numbers, the polyadic Euler function, polyadic division with a…
The present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac-Moody algebras. The resulting quantum symmetric pairs are right coideal subalgebras…
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in…