κ-Deformed Phase Space, Hopf Algebroid and Twisting

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 18 Nov 2014Embargo end date: 01 Jan 2014 Croatia Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659,

Copyright policy )Funded by:EC | RBI-T-WINNING, MZOS | Quantum field theory, non...

Authors: Jurić, Tajron; Kovačević, Domagoj; Meljanac, Stjepan;

doi: 10.3842/sigma.2014.106 , 10.48550/arxiv.1402.0397

arXiv: 1402.0397

κ-Deformed Phase Space, Hopf Algebroid and Twisting

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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 $��$-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 $��$-Poincar�� algebra. Several examples of realizations are worked out in details.

Country

Croatia

Related Organizations

University of Zagreb
Croatia
Ruđer Bošković Institute
Croatia

Keywords

High Energy Physics - Theory, Special relativity, noncommutative space ; κ-Minkowski spacetime ; Hopf algebroid ; κ-Poincaré algebra ; realizations ; twist., Physics, κ-Poincaré algebra, $\kappa$-Poincaré algebra, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Mathematical Physics (math-ph), κ-Minkowski spacetime, NATURAL SCIENCES, High Energy Physics - Theory (hep-th), $\kappa$-Minkowski spacetime, twist, twist., Noncommutative geometry in quantum theory, noncommutative space, Hopf algebroid, Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematical Physics, realizations

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