Description
| Product ID: | 9783642784026 |
| Product Form: | Paperback / softback |
| Country of Manufacture: | GB |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Title: | Quantum Groups and Their Primitive Ideals |
| Authors: | Author: Anthony Joseph |
| Page Count: | 383 |
| Subjects: | Algebra, Algebra, Groups and group theory, Algebraic geometry, Mathematical physics, Groups & group theory, Algebraic geometry, Mathematical physics |
| 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. 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. 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. |
| Imprint Name: | Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Publisher Name: | Springer-Verlag Berlin and Heidelberg GmbH & Co. KG |
| Country of Publication: | GB |
| Publishing Date: | 2011-12-08 |