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arxiv: 0903.5251 · v3 · submitted 2009-03-30 · ✦ hep-th · math-ph· math.MP· math.QA

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Classical basis for kappa-Poincare algebra and doubly special relativity theories

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classification ✦ hep-th math-phmath.MPmath.QA
keywords algebrakappa-poincareclassicalquantumbasisdoublypoincarerelativity
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Several issues concerning quantum kappa-Poincare algebra are discussed and reconsidered here. We propose two different formulations of kappa-Poincare quantum algebra. Firstly we present a complete Hopf algebra formulae of kappa-Poincare in classical Poincare basis. Further by adding one extra generator, which modifies the classical structure of Poincare algebra, we eliminate non polynomial functions in the kappa-parameter. Hilbert space representations of such algebras make Doubly Special Relativity (DSR) similar to the Stueckelberg's version of (proper-time) relativistic Quantum Mechanics.

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  1. Bicovariant Codifferential Calculi

    math.QA 2026-02 unverdicted novelty 6.0

    Bicovariant codifferential calculi on Hopf algebras reduce to classifying Yetter-Drinfeld submodules, providing a dual to existing differential calculi constructions.