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This article is cited in 32 scientific papers (total in 32 papers)
$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
Tajron Jurića, Domagoj Kovačevićb, Stjepan Meljanaca a Rudjer Bošković Institute, Bijenička cesta 54, HR-10000 Zagreb, Croatia
b Faculty of Electrical Engineering and Computing, Unska 3, HR-10000 Zagreb, Croatia
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.
Keywords:
noncommutative space; $\kappa$-Minkowski spacetime; Hopf algebroid; $\kappa$-Poincaré algebra; realizations; twist.
Received: February 21, 2014; in final form November 11, 2014; Published online November 18, 2014
Citation:
Tajron Jurić, Domagoj Kovačević, Stjepan Meljanac, “$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting”, SIGMA, 10 (2014), 106, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma971 https://www.mathnet.ru/eng/sigma/v10/p106
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Abstract page: | 152 | Full-text PDF : | 33 | References: | 26 |
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