Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis

Understand

We consider the Lie group $\mathbb{R}^D_\kappa$ generated by the Lie algebra of $\kappa$-Minkowski space.

• Imposing the invariance of the metric under the pull-back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with $\mathbb{R}^D_\kappa$.
• This metric coincides with the metric of de Sitter space-time.
• We analyze the structure of unitary representations of the group $\mathbb{R}^D_\kappa$ relevant for the realization of the non-commutative $\kappa$-Minkowski space by embedding into $(2D-1)$-dimensional Heisenberg algebra.