Tate-Shafarevich groups and algebras
Group Theory
2025-07-02 v2 Rings and Algebras
Abstract
The Tate-Shafarevich set of a group G defined by Takashi Ono coincides, in the case where G is finite, with the group of outer class-preserving automorphisms of G introduced by Burnside. We consider analogues of this important group-theoretic object for Lie algebras and associative algebras and establish some new structure properties thereof. We also discuss open problems and eventual generalizations to other algebraic structures.
Keywords
Cite
@article{arxiv.2211.05406,
title = {Tate-Shafarevich groups and algebras},
author = {Boris Kunyavskii and Vadim Z. Ostapenko},
journal= {arXiv preprint arXiv:2211.05406},
year = {2025}
}
Comments
14 pages; revised according to the referee's remarks