A construction of symmetric linear functions on the restricted quantum group $\bar{U}_{q}(\mathit{sl}_{2})$

Abstract

In this article we construct all the primitive idempotents of the restricted quantum group $\bar{U}_{q} (\mathit{sl}_{2})$ and also describe $\bar{U}_{q} (\mathit{sl}_{2})$ as the subalgebra of the direct sum of matrix algebras. By using this result we construct a basis of the space of symmetric linear functions of $\bar{U}_{q}(\mathit{sl}_{2})$ and determine the decomposition of the integral of the dual of $\bar{U}_{q} (\mathit{sl}_{2})$ twisted by the balancing element to the basis of the space of symmetric linear functions.