# κ-Deformed Phase Space, Hopf Algebroid and Twisting

@article{Juric2014DeformedPS,
title={$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting},
author={Tajron Juri'c and Domagoj Kovavcevi'c and Stjepan Meljanac},
journal={Symmetry Integrability and Geometry-methods and Applications},
year={2014},
volume={10},
pages={106-124}
}
• Published 3 February 2014
• Mathematics
• Symmetry Integrability and Geometry-methods and Applications
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 e algebra…
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## References

SHOWING 1-10 OF 82 REFERENCES

• Mathematics
• 2012
A bstractWe deform a phase space (Heisenberg algebra and corresponding coalgebra) by twist. We present undeformed and deformed tensor identities that are crucial in our construction. Coalgebras for
• Mathematics
• 2014
The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The κ-deformed phase space with noncommutative coordinates is realized in terms of undeformed
• Mathematics
• 2014
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role
• Mathematics
• 1999
Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B∨ of sl(N) the explicit expressions are obtained for the twist element F,
We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras
• Mathematics
• 2013
We analyze bicovariant differential calculus on κ-Minkowski spacetime. It is shown that corresponding Lorentz generators and noncommutative coordinates compatible with bicovariant calculus cannot be
• Mathematics
• 2012
We unify κ-Minkowki spacetime and Lorentz algebra in unique Lie algebra. Introducing commutative momenta, a family of κ-deformed Heisenberg algebras and κ-deformed Poincaré algebras are defined. They
• Mathematics
• 2009
Several issues concerning the quantum κ-Poincaré algebra are discussed and reconsidered here. We propose two different formulations of the κ-Poincaré quantum algebra. Firstly we present a complete