Hall algebras and the Quantum Frobenius
arXiv:math/0601150 · doi:10.1215/00127094-2010-036
Abstract
Lusztig has constructed a Frobenius morphism for quantum groups at an -th root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. Using the Hall algebra we give a simple construction of this map for the positive part of the quantum group attached to an arbitrary Cartan datum in the nondivisible case.
Final version: typos corrected and exposition improved