We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
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.
