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In this paper we study the tensor category structure of the module categoryof the restricted quantum enveloping algebra associated to $\mathfrak{sl}_2$.Indecomposable decomposition of all tensor products of modules over thisalgebra is completely determined in explicit formulas. As a by-product, we showthat the module category of the restricted quantum enveloping algebraassociated to $\mathfrak{sl}_2$ is not a braided tensor category.

Indecomposable decomposition of tensor products of modules over the  restricted quantum universal enveloping algebra associated to  $\boldsymbol{\mathfrak{sl}_2}$