dS-AdS structures in the non-commutative Minkowski spaces

  title={dS-AdS structures in the non-commutative Minkowski spaces},
  author={M.Olshanetsky and V.Rogov},
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… 



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