Representations of the small quasi-quantum group

Abstract

In this paper, we study the representation theory of the small quantum group Uqand the small quasi-quantum group Uq, where qis a primitive n-th root of unity and n>2is odd. All finite dimensional indecomposable Uq-modules are described and classfied. Moreover, the decomposition rules for the tensor products of Uq-modules are given. Finally, we describe the structures of the projective class ring rp( Uq)and the Green ring r( Uq). We show that r(Uq)is isomorphic to a subring of r( Uq), and the stable Green rings rst( Uq)and rst(Uq)are isomorphic.