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arXiv · 1003.0849

Braided algebras and the kappa-deformed oscillators

Jerzy Lukierski·Mariusz Woronowicz
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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.

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Jerzy Lukierski, Mariusz Woronowicz. 2010-03-03. Braided algebras and the kappa-deformed oscillators. https://doi.org/10.1007/s10714-011-1168-8

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