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1. CMB 1997 (vol 40 pp. 143)

Bremner, Murray
Quantum deformations of simple Lie algebras
It is shown that every simple complex Lie algebra $\fg$ admits a 1-parameter family $\fg_q$ of deformations outside the category of Lie algebras. These deformations are derived from a tensor product decomposition for $U_q(\fg)$-modules; here $U_q(\fg)$ is the quantized enveloping algebra of $\fg$. From this it follows that the multiplication on $\fg_q$ is $U_q(\fg)$-invariant. In the special case $\fg = {\ss}(2)$, the structure constants for the deformation ${\ss}(2)_q$ are obtained from the quantum Clebsch-Gordan formula applied to $V(2)_q \otimes V(2)_q$; here $V(2)_q$ is the simple 3-dimensional $U_q\bigl({\ss}(2)\bigr)$-module of highest weight $q^2$.

Categories:17B37, 17A01

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