Non-commutative amoebas
Complex Variables
2021-02-19 v1
Abstract
The group of isometries of the hyperbolic 3-space is one of the simplest non-commutative complex Lie groups. Its quotient by the maximal compact subgroup naturally maps it back to the hyperbolic space. Each fiber of this map is diffeomorphic to the real projective 3-space. The resulting map can be viewed as the simplest non-commutative counterpart of the amoeba map introduced, in the commutative setting, by Gelfand, Kapranov and Zelevinsky. The paper surveys basic properties of the non-commutative amoebas and compares them against their commutative counterparts.
Cite
@article{arxiv.2102.09324,
title = {Non-commutative amoebas},
author = {Grigory Mikhalkin and Mikhail Shkolnikov},
journal= {arXiv preprint arXiv:2102.09324},
year = {2021}
}