Tate-Shafarevich groups and algebras

Boris Kunyavskiǐ; Vadim Z. Ostapenko

doi:10.1142/s0218196723500364

Tate-Shafarevich groups and algebras

Boris Kunyavskiǐ, Vadim Z. Ostapenko

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 analogs 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.

Original language	English
Pages (from-to)	819-836
Number of pages	18
Journal	International Journal of Algebra and Computation
Volume	33
Issue number	4
DOIs	https://doi.org/10.1142/s0218196723500364
State	Published - 1 Jun 2023

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.

Keywords

Lie algebra
associative algebra
cohomology
derivation

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10.1142/s0218196723500364

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KW - associative algebra

KW - cohomology

KW - derivation

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Tate-Shafarevich groups and algebras

Abstract

Bibliographical note

Keywords

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