---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/LieTheory/QuantumGroups/bibliography.html"
source: "https://docs.magma-maths.org/LieTheory/QuantumGroups/bibliography.md"
part: "Lie Theory"
chapter: "Quantum Groups"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Lie Theory", "source": "../index-lie-theory.md"}
  - {"title": "Quantum Groups", "source": "index-quantum-groups.md"}
prev: {"title": "Homomorphisms to the Universal Enveloping Algebra", "source": "q.md"}
next: {"title": "Groups of Lie Type", "source": "../ChevalleyGroups/index-chevalley-groups.md"}
---

# Bibliography

<a id="cite-graaf01"></a>
- **[Gra01]** W. A. de Graaf. Computing with quantized enveloping algebras: PBW-type bases, highest-weight modules, $R$-matrices. *J. Symbolic Comput.*, 32(5):475–490, 2001.
<a id="cite-graaf02"></a>
- **[Gra02]** W. A. de Graaf. Constructing canonical bases of quantized enveloping algebras. *Experimental Mathematics*, 11(2):161–170, 2002.
<a id="cite-graaf04"></a>
- **[Gra04]** W. A. de Graaf. Five constructions of representations of quantum groups. *Note di Matematica*, 22(1):27–48, 2003/04.
<a id="cite-jantzen96"></a>
- **[Jan96]** J. C. Jantzen. *Lectures on Quantum Groups*. Volume 6 of Graduate Studies in Mathematics. American Mathematical Society, 1996.
<a id="cite-kashiwara96"></a>
- **[Kas96]** M. Kashiwara. Similarity of crystal bases. In *Lie algebras and their representations (Seoul, 1995)*, pages 177–186. Amer. Math. Soc., Providence, RI, 1996.
<a id="cite-littelmann94"></a>
- **[Lit94b]** P. Littelmann. A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras. *Invent. Math.*, 116(1-3):329–346, 1994.
<a id="cite-littelmann95"></a>
- **[Lit95]** P. Littelmann. Paths and root operators in representation theory. *Ann. of Math. (2)*, 142(3):499–525, 1995.
<a id="cite-lusztig90"></a>
- **[Lus90]** G. Lusztig. Quantum groups at roots of $1$. *Geom. Dedicata*, 35(1-3):89–113, 1990.
<a id="cite-lusztig93"></a>
- **[Lus93]** G. Lusztig. *Introduction to quantum groups*. Birkhäuser Boston Inc., Boston, MA, 1993.
<a id="cite-lusztig96"></a>
- **[Lus96]** G. Lusztig. Braid group action and canonical bases. *Adv. Math.*, 122(2):237–261, 1996.