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

Abstract

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

18pages, 1 figure, we modified Section 4 of the first version and added Appendix B to explain known results on representation theory of $\bar{D}$. We also added Appendix A for general facts on finite dimensional Hopf algebras

References in corpus (1)

• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity

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