The elliptic GL(n) dynamical quantum group as an h-Hopf algebroid

Details The elliptic GL(n) dynamical quantum group as an h-Hopf algebroid The elliptic GL(n) dynamical quantum group as an h-Hopf algebroid

2008-03-26

arxiv.org/abs/0803.3815v2

International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 545892, 41 pages, 2009.

Mathematics

Quantum Algebra

38 pages

Scientific paper

10.1155/2009/545892

Using the language of h-Hopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, F_ell(GL(n)), from the elliptic solution of the quantum dynamical Yang-Baxter equation with spectral parameter associated to the Lie algebra sl_n. We apply the generalized FRST construction and obtain an h-bialgebroid F_ell(M(n)). 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 h-Hopf algebroid F_ell(GL(n)).

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