The prime spectrum and representation theory of the 2 × 2 reflection equation algebra

The theory of generalized Weyl algebras is used to study the 2 x 2 reflection equation algebra in the case that q is not a root of unity, where the R-matrix used to define is the standard one of type A. Simple finite-dimensional -modules are classified, finite-dimensional weight modules are shown to be semisimple, is computed, and the prime spectrum of is computed along with its Zariski topology. Finally, it is shown that satisfies the Dixmier-Moeglin equivalence.