https://doi.org/10.1140/epjc/s10052-024-13200-y
Regular Article – Theoretical Physics
Realizations and star-product of doubly 
-deformed Yang models
1
Faculty of Science, University of Split, Ruđera Boškovića 33, 21000, Split, Croatia
2
Division of Theoretical Physics, Ruđer Bošković Institute, Bijenička cesta 54, 10002, Zagreb, Croatia
3
Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy
4
INFN, Sezione di Cagliari, Cittadella Universitaria, 09042, Monserrato, Italy
Received:
14
April
2024
Accepted:
2
August
2024
Published online:
22
August
2024
The Yang algebra was proposed a long time ago as a generalization of the Snyder algebra to the case of curved background spacetime. It includes as subalgebras both the Snyder and the de Sitter algebras and can therefore be viewed as a model of noncommutative curved spacetime. A peculiarity with respect to standard models of noncommutative geometry is that it includes translation and Lorentz generators, so that the definition of a Hopf algebra and the physical interpretation of the variables conjugated to the primary ones is not trivial. In this paper we consider the realizations of the Yang algebra and its -deformed generalization on an extended phase space and in this way we are able to define a Hopf structure and a twist.
© The Author(s) 2024
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