Quantum Groups and Their Primitive Ideals (Paperback, Softcover reprint of the original 1st ed. 1995)

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."

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 29
Release date:	December 2011
First published:	1995
Authors:	Anthony Joseph
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Paperback
Pages:	383
Edition:	Softcover reprint of the original 1st ed. 1995
ISBN-13:	978-3-642-78402-6
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Applied mathematics > General Promotions
LSN:	3-642-78402-X
Barcode:	9783642784026

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