Computation of the Component Group of an Arbitrary Real Algebraic Group

Автор: Timashev D.A.
Журнал: Journal of Mathematical Sciences
Том: 284
Номер: 4
Год издания: 2024
Издательство: Plenum Publishers
Местоположение издательства: United States
Первая страница: 545
Последняя страница: 553
DOI: 10.1007/s10958-024-07369-6
Аннотация: We compute explicitly the group of connected components of the real Lie group G(R) for an arbitrary (not necessarily linear) connected algebraic group G defined over the field R of real numbers. In particular, it turns out that the component group is always an elementary Abelian 2-group. The result looks most transparent in the cases where G is a linear algebraic group or an Abelian variety. The computation is based on structure results on algebraic groups and Galois cohomology methods.
Добавил в систему: Тимашёв Дмитрий Андреевич

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