Tate-Shafarevich groups and algebras. (English) Zbl 1534.17020
Summary: 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.
MSC:
| 17B40 | Automorphisms, derivations, other operators for Lie algebras and super algebras |
| 17B56 | Cohomology of Lie (super)algebras |
| 20J06 | Cohomology of groups |
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