✦ LIBER ✦
Computing with Quantized Enveloping Algebras: PBW-Type Bases, Highest-Weight Modules andR-Matrices
✍ Scribed by W.A. de Graaf
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 367 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0747-7171
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✦ Synopsis
Let Uq(g) be the quantized enveloping algebra corresponding to the semisimple Lie algebra g. We describe algorithms to obtain the multiplication table of a PBW-type basis of Uq(g). We use this to obtain an algorithm for calculating a Gröbner basis of an ideal in the subalgebra U -, which leads to a general construction of irreducible highest-weight modules over Uq(g). We also indicate how to compute the corresponding R-matrices.