On simple modules and automorphisms of the quantum Galilei group

This paper is devoted to ring theoretic properties and representations of the quantum Galilei group Fq(G) and its Hopf dual Uq(g). We classify the primitive ideals and simple modules of Fq(G) and Uq(g) over an algebraically closed field of arbitrary characteristic. We determine their groups of automorphisms over a field of characteristic zero.