Quantum Groups and Their Primitive Ideals Paperback / softback
by Anthony Joseph
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati series
Paperback / softback
Description
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.
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- Format:Paperback / softback
- Pages:383 pages, IX, 383 p.
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:08/12/2011
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- ISBN:9783642784026
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Information
-
Only a few left - usually despatched within 24 hours
- Format:Paperback / softback
- Pages:383 pages, IX, 383 p.
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:08/12/2011
- Category:
- ISBN:9783642784026