QUANTUM GROUPS AND THEIR PRIMITIVE IDEALS by Anthony Joseph ( 9783642784026 )

Item Details

Title:

QUANTUM GROUPS AND THEIR PRIMITIVE IDEALS

By:

Anthony Joseph

Format:

Paperback

List price:

£69.99

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£61.24

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£8.75

ISBN 10:

364278402X

ISBN 13:

9783642784026

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Stock:

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Publisher:

SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG

Pub. date:

8 December, 2011

Edition:

Softcover reprint of the original 1st ed. 1995

Series:

Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3 Folge /A Series of 29

Pages:

392

Synopsis:

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.

Illustrations:

biography

Publication:

Germany

Imprint:

Springer-Verlag Berlin and Heidelberg GmbH & Co. K

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