Geodesic
Quantum Deformations of Simple Lie Algebras
Canadian mathematical bulletin, Tome 40 (1997) no. 2, pp. 143-148

Voir la notice de l'article provenant de la source Cambridge University Press

It is shown that every simple complex Lie algebra g admits a 1-parameter family gq of deformations outside the category of Lie algebras. These deformations are derived from a tensor product decomposition for Uq (g)-modules; here Uq (g) is the quantized enveloping algebra of g. From this it follows that the multiplication on gq is Uq (g)-invariant. In the special case g = (2), the structure constants for the deformation g (2)q are obtained from the quantum Clebsch-Gordan formula applied to V(2)q ⊗ V(2)q; here V(2)q is the simple 3-dimensional Uq (g(2))-module of highest weight q2.
DOI : 10.4153/CMB-1997-017-6
Mots-clés : Primary: 17B37, Secondary: 17A01 
Bremner, Murray. Quantum Deformations of Simple Lie Algebras. Canadian mathematical bulletin, Tome 40 (1997) no. 2, pp. 143-148. doi: 10.4153/CMB-1997-017-6
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[CP] [CP] Chari, V. and Pressley, A., A Guide to Quantum Groups, Cambridge, 1994. Google Scholar

[DH] [DH] Delius, G. W. and A. Ḧuffmann, On quantum Lie algebras and quantum root systems, MSRI preprints on quantum algebra and topology, q-alg/9506017. Google Scholar

[DHGZ] [DHGZ] Delius, G. W., A. Ḧuffmann, Gould, M. D. and Zhang, Y.-Z., Quantum Lie algebras associated to Uq( n) and Uq( n), MSRI preprints on quantum algebra and topology, q-alg/9508013. Google Scholar

[J] [J] Jantzen, J. C., Lectures on Quantum Groups, American Mathematical Society, 1995. Google Scholar

[K] [K] Kassel, C., Quantum Groups, Springer-Verlag, 1995. Google Scholar

[Li] [Li] Liu, K.-Q., Characterizations of the quantum Witt algebra, Lett. Math. Phys. 24 (1992), 257–265. Google Scholar

[Lu] [Lu] Lusztig, G., Introduction to Quantum Groups, Birkhäuser, 1993. Google Scholar

[LS] [LS] Lyubashenko, V. and Sudbery, A., Quantum Lie algebras of type An, MSRI preprints on quantum algebra and topology, q-alg/9510004. Google Scholar

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