Braided algebras and the kappa-deformed oscillators

TL;DR

This paper explores the structure of kappa-deformed oscillator algebras within braided algebra frameworks, focusing on coassociative cases and introducing a new example related to group manifold approaches.

Contribution

It introduces a new example of kappa-deformed oscillators in the group manifold approach and analyzes multilinear extensions consistent with braided algebra axioms.

Findings

Explicit examples of binary kappa-deformed oscillator relations

Description of coassociative multilinear extensions

Introduction of a new oscillator model in group manifold approach

Abstract

Recently there were presented several proposals how to formulate the binary relations describing kappa-deformed oscillator algebras. In this paper we shall consider multilinear products of kappa-deformed oscillators consistent with the axioms of braided algebras. In general case the braided triple products are quasi-associative and satisfy the hexagon condition depending on the coassociator $Phi \in A\otimes A\otimes A$. We shall consider only the products of kappa-oscillators consistent with co-associative braided algebra, with Phi =1. We shall consider three explicite examples of binary kappa-deformed oscillator algebra relations and describe briefly their multilinear coassociative extensions satisfying the postulates of braided algebras. The third example, describing kappa-deformed oscillators in group manifold approach to kappa-deformed fourmomenta, is a new result.