New realizations of Lie algebra kappa-deformed Euclidean space
@article{Meljanac2006NewRO, title={New realizations of Lie algebra kappa-deformed Euclidean space}, author={Stjepan Meljanac and Marko Stoji{\'c}}, journal={The European Physical Journal C - Particles and Fields}, year={2006}, volume={47}, pages={531-539} }
We study Lie algebra κ-deformed Euclidean space with undeformed rotation algebra SOa(n) and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are constructed and a corresponding star product is found for each of them. The κ-deformed noncommutative space of the Lie algebra type with undeformed Poincaré algebra and with the corresponding deformed coalgebra is constructed in a unified way.
137 Citations
Covariant realizations of kappa-deformed space
- Mathematics
- 2007
We study a Lie algebra type κ-deformed space with an undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. The space deformation depends on an arbitrary…
Kappa-deformed Snyder spacetime
- Mathematics
- 2009
We present Lie-algebraic deformations of Minkowski space with undeformed Poincare algebra. These deformations interpolate between Snyder and kappa-Minkowski space. We find realizations of…
κ-deformation of phase space; generalized Poincaré algebras and R-matrix
- MathematicsJournal of High Energy Physics
- 2012
We 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 the…
Twisted exterior derivatives for enveloping algebras
- Mathematics
- 2008
We extend the representations of finite-dimensional Lie algebra by derivations of the completed symmetric algebra of its dual to the derivations of a bigger algebra which includes the exterior…
Generalized kappa-deformed spaces, star products and their realizations
- Mathematics
- 2008
In this work we investigate generalized kappa-deformed spaces. We develop a systematic method for constructing realizations of noncommutative (NC) coordinates as formal power series in the Weyl…
κ-deformation of phase space; generalized Poincaré algebras and R-matrix
- 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…
DIFFERENTIAL ALGEBRAS ON κ-MINKOWSKI SPACE AND ACTION OF THE LORENTZ ALGEBRA
- Mathematics
- 2012
We propose two families of differential algebras of classical dimension on κ-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl…
Lie algebraic deformations of Minkowski space with Poincare algebra
- Mathematics
- 2009
We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of…
Lie algebra type noncommutative phase spaces are Hopf algebroids
- 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…
Twisted exterior derivatives for enveloping algebras
- Mathematics
- 2008
Consider any representation φ of a finite-dimensional Lie algebra g by derivations of the completed symmetric algebra Ŝ(g) of its dual. Consider the tensor product of Ŝ(g∗) and the exterior algebra…
References
SHOWING 1-10 OF 51 REFERENCES
New Lie-algebraic and quadratic deformations of Minkowski space from twisted Poincaré symmetries
- Mathematics
- 2006
Deformed field theory on $\kappa$-spacetime
- Mathematics
- 2003
Abstract.A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (the Poincaré…
Local field theory on κ-Minkowski space, star products and noncommutative translations
- Mathematics
- 2000
We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed…
Gauge theories on the $\kappa$-Minkowski spacetime
- Mathematics, Physics
- 2003
Abstract.This study of gauge field theories on $\kappa$-deformed Minkowski spacetime extends previous work on field theories on this example of a non-commutative spacetime. We construct deformed…
Derivatives, forms and vector fields on the κ-deformed Euclidean space
- Mathematics
- 2004
The model of κ-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper, we present new results concerning different sets of derivatives…
Deformed Heisenberg algebras, a Fock-space representation and the Calogero model
- Physics
- 2000
Abstract. We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed…