Work

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

Year: 2009

Type: article

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)).

Source: International Journal of Mathematics and Mathematical Sciences

DOI: 10.1155/2009/545892

Author: Jonas T. Hartwig

Institution: University of Amsterdam

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,240

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek