By Anthony Joseph
Through a extra basic quadratic algebra (possibly bought by way of deformation) after which to derive Rq [G] via requiring it to own the latter as a comodule. a 3rd precept is to concentration realization at the tensor constitution of the cat egory of (!; modules. this suggests after all simply defining an algebra constitution on Rq[G]; yet this can be to be performed in a truly particular demeanour. Concretely the class is needed to be braided and this forces (9.4.2) the life of an "R-matrix" fulfilling specifically the quantum Yang-Baxter equation and from which the algebra constitution of Rq[G] may be written down (9.4.5). eventually there has been a look for a superbly self-dual version for Rq[G] which might then be isomorphic to Uq(g). it sounds as if this failed; yet V. G. Drinfeld discovered that it may be basically made to paintings for the "Borel half" of Uq(g) denoted U (b) and extra stumbled on a basic development (the Drinfeld double) q mirroring a Lie bialgebra. this offers Uq(g) as much as passage to a quotient. some of the most extraordinary facets of the above superficially diversified ap proaches is their striking intercoherence. particularly they primarily all lead for G semisimple to an analogous and consequently "canonical", items Rq[G] and Uq(g), even though this epithet may possibly as but be untimely.
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