Monoidal structure of the category of u$_q^+$-modules

Details Monoidal structure of the category of u$_q^+$-modules Monoidal structure of the category of u$_q^+$-modules

2000-10-12

arxiv.org/abs/math/0010116v1

Mathematics

Quantum Algebra

18 pages

Scientific paper

We study the finite dimensional modules on the half-quantum group u_q^+ at a root of unity q, whose action can be extended to u_q (quotient of the quantized enveloping algebra of sl_2). We derive decomposition formulas of the tensor product of indecomposable u_q^+-modules, which includes the cases of the universal and the quantized universal enveloping algebra of sl_2 for q not a root of unity. We also prove that simple modules on u_q correspond exactly to the extendable non projective u_q^+-modules. We thus establish decomposition formulas for the tensor product of simple u_q-modules.

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