# dS-AdS structures in the non-commutative Minkowski spaces

@inproceedings{MOlshanetsky2004dSAdSSI, title={dS-AdS structures in the non-commutative Minkowski spaces}, author={M.Olshanetsky and V.Rogov}, year={2004} }

We consider a family of non-commutative 4d Minkowski spaces with the signature (1,3) and two types of spaces with the signature (2,2). The Minkowski spaces are deﬁned by the common reﬂection equation and diﬀer in anti-involutions. There exist two Casimir elements and the ﬁxing of one of them leads to the non-commutative ”homogeneous” spaces H 3 , dS 3 , AdS 3 and light-cones. We present the quasi-classical description of the Minkowski spaces. There are three compatible Poisson structures…

## References

SHOWING 1-10 OF 16 REFERENCES

### Tensor representation of the quantum groupSLq(2,C) and quantum Minkowski space

- Mathematics
- 1990

We investigate the structure of the tensor product representation of the quantum groupSLq(2,C) by using the 2-dimensional quantum plane as a building block. Two types of 4-dimensional spaces are…

### q-deformed de Sitter/conformal field theory correspondence

- Mathematics
- 2004

Unitary principal series representations of the conformal group appear in the de Sitter/conformal field theory (dS/CFT) correspondence. These are infinite-dimensional irreducible representations,…

### A new twist on dS/CFT

- Mathematics
- 2003

We stress that the dS/CFT correspondence should be formulated using unitary principal series representations of the de Sitter isometry group/conformal group, rather than highest-weight…

### Deformed Minkowski spaces: classification and properties

- Mathematics
- 1996

Using general but simple covariance arguments, we classify the `quantum' Minkowski spaces for dimensionless deformation parameters. This requires a previous analysis of the associated Lorentz groups,…

### New q-Minkowski space-time and q-Maxwell equations hierarchy from q-conformal invariance

- Mathematics
- 1994

### Finite number of states, de Sitter space and quantum groups at roots of unity

- Physics
- 2004

This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was…

### Representations of q-Minkowski space algebra

- Mathematics
- 1993

The properties of the quantum Minkowski space algebra are discussed. Its irreducible representations with highest weight vectors are constructed and relations to other quantum algebras: $su_{q}(2)$,…

### Fe b 20 01 ITEP-TH-8 / 01 Unitary representations of U q ( sl ( 2 , R ) ) , the modular double , and the multiparticle q-deformed Toda chains

- Mathematics
- 2001

The paper deals with the analytic theory of the quantum q -deformed Toda chains; the technique used combines the methods of representation theory and the Quantum Inverse Scattering Method. The key…

### Quantum linear problem for the sine-Gordon equation and higher representations

- Mathematics
- 1983

A quantum linear problem is constructed which permits the investigation of the sine-Gordon equation within the framework of the inverse scattering method in an arbitrary representation of algebra.…