Quantum Groups and Their Primitive Ideals [electronic resource] /

by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat­ egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap­ proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature.

Bibliographic Details

Main Authors:	Joseph, Anthony. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg, 1995
Subjects:	Mathematics., Algebraic geometry., Associative rings., Rings (Algebra)., Nonassociative rings., Topological groups., Lie groups., Physics., Non-associative Rings and Algebras., Associative Rings and Algebras., Topological Groups, Lie Groups., Algebraic Geometry., Theoretical, Mathematical and Computational Physics.,
Online Access:	http://dx.doi.org/10.1007/978-3-642-78400-2
Tags:	Add Tag No Tags, Be the first to tag this record!