Tate-Shafarevich groups and algebras

Boris Kunyavskiǐ, Vadim Z. Ostapenko

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1 Scopus citations


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 languageEnglish
Pages (from-to)819-836
Number of pages18
JournalInternational Journal of Algebra and Computation
Issue number4
StatePublished - 1 Jun 2023

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  • associative algebra
  • cohomology
  • derivation
  • Lie algebra


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