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Dual $κ$-Minkowski spaces and $κ$-Poincaré algebras from Yang model and their Weyl realizations

T. Martinić Bilać, S. Meljanac, S. Mignemi

Abstract

We consider the Yang algebras isomorphic to $o(1,5), o(2,4), o(3,3)$ and derive dual $κ$-Minkowski and $κ$-Poincaré algebras in terms of a metric $g$. The corresponding Weyl realization is presented and coproduct, star product and twist are computed in terms of the metric $g$. Finally, we construct reduced $κ$-Minkowski and $κ$-Poincaré algebras as special cases.

Dual $κ$-Minkowski spaces and $κ$-Poincaré algebras from Yang model and their Weyl realizations

Abstract

We consider the Yang algebras isomorphic to and derive dual -Minkowski and -Poincaré algebras in terms of a metric . The corresponding Weyl realization is presented and coproduct, star product and twist are computed in terms of the metric . Finally, we construct reduced -Minkowski and -Poincaré algebras as special cases.
Paper Structure (15 sections, 145 equations)

This paper contains 15 sections, 145 equations.

Table of Contents

  1. Introduction
  2. Generalized Yang models isomorphic to $o(1,5,g)$
  3. Dual $\kappa$-Minkowski spaces and $\kappa$-Poincaré algebras isomorphic to $o(1,5,g)$
  4. Generalized Yang models isomorphic to $o(2,4,g)$
  5. Dual $\kappa$-Minkowski spaces and $\kappa$-Poincaré algebras isomorphic to $o(2,4,g)$
  6. Generalized Yang models isomorphic to $o(3,3,g)$
  7. Dual $\kappa$-Minkowski spaces and $\kappa$-Poincaré algebras isomorphic to $o(3,3,g)$
  8. Unification of the four cases $\epsilon_{1} = \pm 1,\; \epsilon_{2} = \pm 1$
  9. Weyl realization for generalized Yang model and dual $\kappa$-Minkowski spaces
  10. Weyl realizations for $o(1,5),\; o(2,4), \; o(3,3)$ algebras
  11. Weyl realizations for $o(1,5, g),\; o(2,4, g)\;$ and $\; o(3,3, g)\;$ algebras
  12. Weyl realization for dual $\kappa$ Minkowski spaces
  13. Coproduct, star product and twist in Weyl realization
  14. Reduced dual $\kappa$-Minkowski spaces and $\kappa$- Poincaré algebras
  15. Concluding remarks