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International Journal of Mathematics and Mathematical Sciences
Volume 2009, Article ID 545892, 41 pages
Research Article

The Elliptic Dynamical Quantum Group as an -Hopf Algebroid

Korteweg-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.


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