The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid

Abstract

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