Toward quantization of Galois theory
Quantum Algebra
2016-09-29 v3
Abstract
This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1. The fundamental question is whether there exists a Galois theory, in which the Galois group is a quantum group. For a linear equations with respect to a Hopf algebra, we arrived at a final form if the base field consists of constants. In this case, we have non-commutative Picard-Vessiot rings and asymmetric Tannaka theory. For non-linear equations there are examples that might make us optimistic.
Cite
@article{arxiv.1501.06668,
title = {Toward quantization of Galois theory},
author = {Akira Masuoka and Katsunori Saito and Hiroshi Umemura},
journal= {arXiv preprint arXiv:1501.06668},
year = {2016}
}
Comments
101 pages, we added Part III, arXiv admin note: text overlap with arXiv:1212.3392, arXiv:1312.4682