Classification of involutive commutative two-valued groups
Group Theory
2023-02-14 v1 Commutative Algebra
Abstract
A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated involutive commutative two-valued group is isomorphic to a two-valued group belonging to one of these series. A number of classification results are obtained for topological involutive commutative two-valued groups in the Hausdorff and locally compact cases. The classification of algebraic involutive two-valued groups in the one-dimensional case is also discussed.
Cite
@article{arxiv.2302.05909,
title = {Classification of involutive commutative two-valued groups},
author = {Victor M. Buchstaber and Alexander A. Gaifullin and Alexander P. Veselov},
journal= {arXiv preprint arXiv:2302.05909},
year = {2023}
}
Comments
67 pages; slightly amended English version of the paper published in Uspekhi Matematicheskikh Nauk (Russian Math Surveys)