Un scindage du morphisme de Frobenius quantique
Representation Theory
2015-06-15 v2 Quantum Algebra
Abstract
We show that the quantum Frobenius morphism constructed by Lusztig in the setting of the quantum enveloping algebra specialized at a root of unity admits a multiplicative splitting (non unital). We also find a basis of the toral part of the small quantum algebra consisting of pairwise orthogonal idempotents summing up to 1, and likewise in the modular case of the algebra of distributions for a semisimple algebraic group.
Cite
@article{arxiv.1302.2437,
title = {Un scindage du morphisme de Frobenius quantique},
author = {Michel Gros and Masaharu Kaneda},
journal= {arXiv preprint arXiv:1302.2437},
year = {2015}
}
Comments
Thanks to enlightning comments of Prof. Yoshihisa Saito on v.1, the proof of thm. 1.5 has been simplified with misprints/Inacuracies corrected