The Elliptic Dynamical Quantum Group as an -Hopf AlgebroidReport as inadecuate




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International Journal of Mathematics and Mathematical SciencesVolume 2009 2009, Article ID 545892, 41 pages

Research ArticleKorteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands

Received 17 May 2009; Accepted 3 August 2009

Academic Editor: Francois Goichot

Copyright © 2009 Jonas T. Hartwig. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using the language of -Hopf algebroids which wasintroduced by Etingof and Varchenko,we construct a dynamical quantum group, ,from the elliptic solution of the quantum dynamical Yang-Baxterequation with spectral parameter associated to theLie algebra . We apply the generalized FRST constructionand obtain an -bialgebroid . Natural analogs ofthe exterior algebra and their matrix elements, elliptic minors,are defined and studied. We show how to use the cobraiding to prove that the elliptic determinantis central. Localizing at this determinant and constructing an antipode we obtain the -Hopf algebroid .





Author: Jonas T. Hartwig

Source: https://www.hindawi.com/



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