Lattices in some symplectic or affine nilpotent Lie groups
نویسندگان
چکیده
منابع مشابه
Affine Actions on Nilpotent Lie Groups
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 ...
متن کاملRiemannian Submersions and Lattices in 2-step Nilpotent Lie Groups
We consider simply connected, 2-step nilpotent Lie groups N, all of which are diffeomorphic to Euclidean spaces via the Lie group exponential map exp : ˆ → N. We show that every such N with a suitable left invariant metric is the base space of a Riemannian submersion ρ : N* → N, where the fibers of ρ are flat, totally geodesic Euclidean spaces. The left invariant metric and Lie algebra of N* ar...
متن کاملCurvature in Nilpotent Lie Groups
Colloq. Algebraic Topology, 1962, pp. 104-113, Matematisk Institut, Aarhus Universitet, Denmark. 4. M. F. Atiyah, Thorn complexes, Proc. London Math. Soc. (3) 11 (1961), 291310. 5. M. F. Atiyah and J. A. Todd, On complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 56 (1960), 342-353. 6. Sze-Tsen Hu, Homotopy theory, Pure and Applied Mathematics VIII, Academic Press, New York and London, 195...
متن کاملApproximate Multiplicative Groups in Nilpotent Lie Groups
We generalize a result of Tao which describes approximate multiplicative groups in the Heisenberg group. We extend it to simply connected nilpotent Lie groups of arbitrary step.
متن کاملCharacteristically Nilpotent Lie Algebras and Symplectic Structures
We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space H(g, k) for certain Lie algebras g. Among these Lie algebras are filiform CNLAs of dimension n ≤ 14. It turns out that there are many examples of CNLAs which admit a symplectic structure. A generalization of a sympletic structure is an affine structure on a Lie algebra.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2014
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2014.03.006