| Quantum Groups and Their Primitive Ideals Softcover Repri Edition Contributor(s): Joseph, Anthony (Author) |
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ISBN: 364278402X ISBN-13: 9783642784026 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Mathematics | Group Theory - Mathematics | Algebra - Abstract |
| Dewey: 512.55 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge / |
| Physical Information: 0.82" H x 6.14" W x 9.21" (1.23 lbs) 383 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |