Monoidal structure of the category of u+q-modules Original Research Article

We study the finite dimensional modules on the half-quantum group u+q at a root of unity q whose action can be extended to uq, quotient of the quantized enveloping algebra of image. We derive decomposition formulas of the tensor product of indecomposable u+q-modules, which includes the cases of the universal and the quantum universal enveloping algebra of image for q not a root of unity. We also prove that simple modules of non-maximal dimension on uq correspond exactly to the indecomposable extendable non-projective u+q-modules. We thus establish decomposition formulas for the tensor product of simple uq-modules.