Geometric interpretation of Planck-scale-deformed co-products

For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of $κ$-Poincaré-inspired and (2+1)-dimensional gravity-inspired composition laws both satisfy our condition. Future applications might include the proposal of a class of models based on momenta spaces with anti-de Sitter geometry.

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