Monoidal structure of the category of uq+-modules

الأصل · EN

We study the finite dimensional modules on the half-quantum group uq+ at a root of unity q, whose action can be extended to uq (quotient of the quantized enveloping algebra of sl₂). We derive decomposition formulas of the tensor product of indecomposable uq+-modules, which includes the cases of the universal and the quantized universal enveloping algebra of sl₂ for q not a root of unity. We also prove that simple modules on uq correspond exactly to the extendable non projective uq+-modules. We thus establish decomposition formulas for the tensor product of simple uq-modules.