Affine actions on nilpotent Lie groups
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Dietrich Burde
Abstract
To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff (N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations.
We succeed in translating the existence question of such a simply transitive affine action to a corresponding question on the Lie algebra level. As an example of the possible use of this translation, we then consider the case where dim(G) = dim(N) ≤ 5.
Finally, we specialize to the case of abelian simply transitive affine actions on a given connected and simply connected nilpotent Lie group. It turns out that such a simply transitive abelian affine action on N corresponds to a particular Lie compatible bilinear product on the Lie algebra 𝔫 of N, which we call an LR-structure.
© de Gruyter 2009
Articles in the same Issue
- Applications of Multivariate Asymptotics I: Boundedness of a maximal operator on
- Geodesic flow of the averaged controlled Kepler equation
- Hyperbolicity in unbounded convex domains
- Explicit connections with SU(2)-monodromy
- Eigentheory of Cayley-Dickson algebras
- Alternators in the Cayley-Dickson algebras
- Cohomological characterisation of Steiner bundles
- Sigma-cotorsion modules over valuation domains
- Affine actions on nilpotent Lie groups
- On the birational geometry of moduli spaces of pointed curves
Articles in the same Issue
- Applications of Multivariate Asymptotics I: Boundedness of a maximal operator on
- Geodesic flow of the averaged controlled Kepler equation
- Hyperbolicity in unbounded convex domains
- Explicit connections with SU(2)-monodromy
- Eigentheory of Cayley-Dickson algebras
- Alternators in the Cayley-Dickson algebras
- Cohomological characterisation of Steiner bundles
- Sigma-cotorsion modules over valuation domains
- Affine actions on nilpotent Lie groups
- On the birational geometry of moduli spaces of pointed curves
