Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to sl2

We study the tensor structure of the category of finite-dimensional modules of the restricted quantum enveloping algebra associated to sl2. Tensor product decomposition rules for all indecomposable modules are explicitly given. As a by-product, it is also shown that the category of finite-dimensional modules of the restricted quantum enveloping algebra associated to sl2 is not a braided tensor category.