Abstract
Around 1985, V. G. Drinfel’d and M. Jimbo introduced the quantized universal enveloping algebras, or quantum groups, U q (g) associated to any symmetrizable Kac-Moody algebra g. Usually, the deformation parameter q is taken to be a non-zero complex number, and one thinks of U q (g) as a family of Hopf algebras over ℂ ‘depending’ on q. If q = 1, one recovers the classical universal enveloping algebra of g. But one can also work ‘universally’, by regarding q as an indeterminate and U q (g) as a Hopf algebra over the field ℂ(q) of rational functions of q (or some larger field).
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