Monoidal structure of the category of u$_q^+$modules
Abstract
We study the finite dimensional modules on the halfquantum 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_qmodules.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2000
 DOI:
 10.48550/arXiv.math/0010116
 arXiv:
 arXiv:math/0010116
 Bibcode:
 2000math.....10116G
 Keywords:

 Quantum Algebra;
 Representation Theory;
 20G42;
 18D10
 EPrint:
 18 pages