Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 106, 18 pages      arXiv:1402.0397      https://doi.org/10.3842/SIGMA.2014.106
Contribution to the Special Issue on Deformations of Space-Time and its Symmetries

$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting

Tajron Jurić a, Domagoj Kovačević b and Stjepan Meljanac a
a) Rudjer Bošković Institute, Bijenička cesta 54, HR-10000 Zagreb, Croatia
b) University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, HR-10000 Zagreb, Croatia

Received February 21, 2014, in final form November 11, 2014; Published online November 18, 2014

Abstract
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.

Key words: noncommutative space; $\kappa$-Minkowski spacetime; Hopf algebroid; $\kappa$-Poincaré algebra; realizations; twist.

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