The Cell Modules of the Green Algebra of Drinfel'd Quantum Double D(H_(4))

This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H_(4))),where D(H_(4))is the Drinfel'd quantum double of Sweedler's 4-dimensional Hopf algebra H_(4).We show that R(D(H_(4)))has one infinite dimensional cell module,one 4-dimensional cell module generated by all finite dimensional indecomposable projective modules of D(H_(4))and infinitely many 2-dimensional cell modules.More precisely,we obtain the decompositions of all finite dimensional cell modules into the direct sum of indecomposable submodules,and show that the infinite dimensional cell module can be written as the direct sum of two infinite dimensional indecomposable submodules.