Displaying similar documents to “On holomorphically separable complex solv-manifolds”

Transitive riemannian isometry groups with nilpotent radicals

C. Gordon (1981)

Annales de l'institut Fourier

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Given that a connected Lie group G with nilpotent radical acts transitively by isometries on a connected Riemannian manifold M , the structure of the full connected isometry group A of M and the imbedding of G in A are described. In particular, if G equals its derived subgroup and its Levi factors are of noncompact type, then G is normal in A . In the special case of a simply transitive action of G on M , a transitive normal subgroup G ' of A is constructed with dim G ' = dim G and a sufficient condition...

An obstruction to homogeneous manifolds being Kähler

Bruce Gilligan (2005)

Annales de l’institut Fourier

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Let G be a connected complex Lie group, H a closed, complex subgroup of G and X : = G / H . Let R be the radical and S a maximal semisimple subgroup of G . Attempts to construct examples of noncompact manifolds X homogeneous under a nontrivial semidirect product G = S ⋉ R with a not necessarily G -invariant Kähler metric motivated this paper. The S -orbit S / S ∩ H in X is Kähler. Thus S ∩ H is an algebraic subgroup of S [4]. The Kähler assumption on X ought to imply the S -action on the base Y of any homogeneous fibration...

Admissibility for quasiregular representations of exponential solvable Lie groups

Vignon Oussa (2013)

Colloquium Mathematicae

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Let N be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra of dimension n. Let H be a subgroup of the automorphism group of N. Assume that H is a commutative, simply connected, connected Lie group with Lie algebra . Furthermore, assume that the linear adjoint action of on is diagonalizable with non-purely imaginary eigenvalues. Let τ = I n d H N ⋊ H 1 . We obtain an explicit direct integral decomposition for τ, including a description of the spectrum as a submanifold of...

Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu (1980)

Annales de l'institut Fourier

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We introduce a new class of connected solvable Lie groups called H -group. Namely a H -group is a connected solvable Lie group with center Z such that for some ℓ in the Lie algebra h of H , the symplectic for B ℓ on h / z given by ℓ ( [ x , y ] ) is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group G with center Z , such that the center of G / Rad G is finite, has discrete series if and only if G may be written as G = H S ' , H ∩ S = Z 0 , where H is a H -group with...

Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center

Bin Ren, Lin Sheng Zhu (2017)

Czechoslovak Mathematical Journal

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A Lie algebra L is called 2-step nilpotent if L is not abelian and [ L , L ] lies in the center of L . 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center.

An application of Lie groupoids to a rigidity problem of 2-step nilmanifolds

Hamid-Reza Fanaï, Atefeh Hasan-Zadeh (2019)

Mathematica Bohemica

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We study a problem of isometric compact 2-step nilmanifolds M / Γ using some information on their geodesic flows, where M is a simply connected 2-step nilpotent Lie group with a left invariant metric and Γ is a cocompact discrete subgroup of isometries of M . Among various works concerning this problem, we consider the algebraic aspect of it. In fact, isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, namely by normalizers. So, suitable...

Fixed points of discrete nilpotent group actions on S 2

Suely Druck, Fuquan Fang, Sebastião Firmo (2002)

Annales de l’institut Fourier

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We prove that for each integer k ≥ 2 there is an open neighborhood 𝒱 k of the identity map of the 2-sphere S 2 , in C 1 topology such that: if G is a nilpotent subgroup of Diff 1 ( S 2 ) with length k of nilpotency, generated by elements in 𝒱 k , then the natural G -action on S 2 has nonempty fixed point set. Moreover, the G -action has at least two fixed points if the action has a finite nontrivial orbit.