Mathematics – Quantum Algebra
Scientific paper
2009-01-27
Mathematics
Quantum Algebra
18pages, 1 figure, we modified Section 4 of the first version and added Appendix B to explain known results on representation
Scientific paper
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.
Kondo Hiroki
Saito Yoshihisa
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