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

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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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     title = {Quantum {Deformations} of {Simple} {Lie} {Algebras}},
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     year = {1997},
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     doi = {10.4153/CMB-1997-017-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-017-6/}
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