# 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…

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