Symmetric linear functions of the restricted quantum group $\bar{U}_qsl_2(\mathbb{C})$

We determine a set of primitive idempotents and the basic algebra of the restricted quantum group $\bar{U}_qsl_2(\mathbb{C})$. As a result, we can show the dimension of the space of symmetric linear functions of $\bar{U}_qsl_2(\mathbb{C})$ is $3p-1$