Non-Commutative Space-Time Geometry and Principle of Gauge Invariance

The realization of the two-dimensional Poincare algebra in terms of the noncommutative differential calculus on the commutative algebra of functions is considered. Corresponding algebra of functions is commutative and is defined by the spectrum of unitary irreducible representations of the two-dimensional De Sitter group. Gauge invariance principle consistent with this quantum geometry is considered