Simply transitive NIL-affine actions of solvable Lie groups
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Jonas Deré
Abstract
Every simply connected and connected solvable Lie group đș admits a simply transitive action on a nilpotent Lie group đ» via affine transformations.
Although the existence is guaranteed, not much is known about which Lie groups đș can act simply transitively on which Lie groups đ».
So far, the focus was mainly on the case where đș is also nilpotent, leading to a characterization depending only on the corresponding Lie algebras and related to the notion of post-Lie algebra structures.
This paper studies two different aspects of this problem.
First, we give a method to check whether a given action
Funding source: Fonds Wetenschappelijk Onderzoek
Award Identifier / Grant number: G.0F93.17N
Funding source: Australian Research Council
Award Identifier / Grant number: DP190100317
Funding statement: The first author is supported by a postdoctoral fellowship of the Research Foundation â Flanders (FWO). The second author was supported by the Research Foundation â Flanders (FWO Project G.0F93.17N), CONICET (Argentina) and ARC (Australia) DP190100317.
Acknowledgements
Most of the work has been written during the post-doctoral position at KU Leuven, Campus Kulak Kortrijk of the second named author. He is grateful to the department for the hospitality.
Communicated by: Anna Wienhard
References
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Articles in the same Issue
- Frontmatter
- Indecomposable involutive solutions of the YangâBaxter equation of multipermutational level 2 with abelian permutation group
- Extrapolation to product Herz spaces and some applications
- The exact number of orthogonal exponentials on the spatial Sierpinski gasket
- A note on special cubic fourfolds of small discriminants
- Strong multiplicity one for Siegel cusp forms of degree two
- GrossâPrasad periods for reducible representations
- LS-category of moment-angle manifolds and higher order Massey products
- Estimates of heat kernels of non-symmetric LĂ©vy processes
- Global continuity of variational solutions weakening the one-sided bounded slope condition
- Finitary birepresentations of finitary bicategories
- Solvability for nonlocal boundary value problems with generalized đ-Laplacian on an unbounded domain
- Conformal Killing forms on 2-step nilpotent Riemannian Lie groups
- Simply transitive NIL-affine actions of solvable Lie groups
- Mahler measure of 3D LandauâGinzburg potentials
Articles in the same Issue
- Frontmatter
- Indecomposable involutive solutions of the YangâBaxter equation of multipermutational level 2 with abelian permutation group
- Extrapolation to product Herz spaces and some applications
- The exact number of orthogonal exponentials on the spatial Sierpinski gasket
- A note on special cubic fourfolds of small discriminants
- Strong multiplicity one for Siegel cusp forms of degree two
- GrossâPrasad periods for reducible representations
- LS-category of moment-angle manifolds and higher order Massey products
- Estimates of heat kernels of non-symmetric LĂ©vy processes
- Global continuity of variational solutions weakening the one-sided bounded slope condition
- Finitary birepresentations of finitary bicategories
- Solvability for nonlocal boundary value problems with generalized đ-Laplacian on an unbounded domain
- Conformal Killing forms on 2-step nilpotent Riemannian Lie groups
- Simply transitive NIL-affine actions of solvable Lie groups
- Mahler measure of 3D LandauâGinzburg potentials
