Source: Osaka J. Math. Volume 47, Number 2
(2010), 535-557.
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.
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