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$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for $\kappa$-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of $\kappa$-Poincaré algebra. Several examples of realizations are worked out in details.
Keywords: noncommutative space; $\kappa$-Minkowski spacetime; Hopf algebroid; $\kappa$-Poincaré algebra; realizations; twist. 
@article{SIGMA_2014_10_a105,
     author = {Tajron Juri\'c and Domagoj Kova\v{c}evi\'c and Stjepan Meljanac},
     title = {$\kappa${-Deformed} {Phase} {Space,} {Hopf} {Algebroid} and {Twisting}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
     volume = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a105/}
}
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Tajron Jurić; Domagoj Kovačević; Stjepan Meljanac. $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a105/

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