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The Elliptic Dynamical Quantum Group as an -Hopf Algebroid

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  • Jonas T. Hartwig

Abstract

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 .

Suggested Citation

  • Jonas T. Hartwig, 2009. "The Elliptic Dynamical Quantum Group as an -Hopf Algebroid," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-41, September.
    • Handle: RePEc:hin:jijmms:545892
    DOI: 10.1155/2009/545892
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