English

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

R2 v1 2026-06-28T05:34:44.466Z