On the centre of a transitive semisimple lie group
Copyright policy )On the centre of a transitive semisimple lie group
The paper deals with the study of the connected semisimple Lie groups acting transitively and effectively on a simply connected compact homogeneous manifold or a noncompact homogeneous manifold with two ends. The author establishes several results about the order and the rank of such a Lie group G. In the case that G acts effectively on a compact homogeneous space and \(| Z(G)| =\infty\) (the center of G is infinite), the Lie algebra of G is determined.
- Yaroslavl State University Russian Federation
Compact Lie groups of differentiable transformations, Lie algebra, Lie algebras of Lie groups, Semisimple Lie groups and their representations, simply connected compact homogeneous manifold, rank, Differential geometry of homogeneous manifolds, center, noncompact homogeneous manifold with two ends, order, Noncompact Lie groups of transformations, semisimple Lie groups acting transitively and effectively on a simply connected compact homogeneous manifold, semisimple Lie groups acting transitively and effectively on a
Compact Lie groups of differentiable transformations, Lie algebra, Lie algebras of Lie groups, Semisimple Lie groups and their representations, simply connected compact homogeneous manifold, rank, Differential geometry of homogeneous manifolds, center, noncompact homogeneous manifold with two ends, order, Noncompact Lie groups of transformations, semisimple Lie groups acting transitively and effectively on a simply connected compact homogeneous manifold, semisimple Lie groups acting transitively and effectively on a
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