The FRT-Construction via Quantum Affine Algebras and Smash Products
Quantum Algebra
2011-05-02 v1
Abstract
For every element w in the Weyl group of a simple Lie algebra g, De Concini, Kac, and Procesi defined a subalgebra U_q^w of the quantized universal enveloping algebra U_q(g). The algebra U_q^w is a deformation of the universal enveloping algebra U(n_+\cap w.n_-). We construct smash products of certain finite-type De Concini-Kac-Procesi algebras to obtain ones of affine type; we have analogous constructions in types A_n and D_n. We show that the multiplication in the affine type De Concini-Kac-Procesi algebras arising from this smash product construction can be twisted by a cocycle to produce certain subalgebras related to the corresponding Faddeev-Reshetikhin-Takhtajan bialgebras.
Keywords
Cite
@article{arxiv.1104.5529,
title = {The FRT-Construction via Quantum Affine Algebras and Smash Products},
author = {Garrett Johnson and Chris Nowlin},
journal= {arXiv preprint arXiv:1104.5529},
year = {2011}
}
Comments
15 pages