Left-Invariant Affine Structures on Reductive Lie Groups
نویسندگان
چکیده
منابع مشابه
Left Invariant Contact Structures on Lie Groups
A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations. The problem of finding which Lie groups admit a left invariant contact structure (contact Lie groups), is then still wide open. We perform a ‘contactization’ method to construct, in every odd dimension...
متن کاملAffine structures on abelian Lie Groups
The Nagano-Yagi-Goldmann theorem states that on the torus T, every affine (or projective) structure is invariant or is constructed on the basis of some Goldmann rings [N-Y]. It shows the interest to study the invariant affine structure on the torus T or on abelian Lie groups. Recently, the works of Kim [K] and Dekempe-Ongenae [D-O] precise the number of non equivalent invariant affine structure...
متن کاملControllability of affine right-invariant systems on solvable Lie groups
First we recall definitions and state our problem. Let G be a real connected Lie group, L be its Lie algebra (i.e. the set of all right-invariant vector fields on G). For any A;B1; : : : ; Bm 2 L we consider the corresponding affine right-invariant system = fA+ m Xi=1 uiBi j 8i ui 2 Rg The attainable set A for the system is a subsemigroup of G generated by one-parameter semigroups f exp(tX) j X...
متن کاملA remark on left invariant metrics on compact Lie groups
The investigation of manifolds with non-negative sectional curvature is one of the classical fields of study in global Riemannian geometry. While there are few known obstruction for a closed manifold to admit metrics of non-negative sectional curvature, there are relatively few known examples and general construction methods of such manifolds (see [Z] for a detailed survey). In this context, it...
متن کاملGerbes on Complex Reductive Lie Groups
Let K be a compact Lie group with complexification G. We construct by geometric methods a conjugation invariant gerbe on G; this then gives by restriction an invariant gerbe on K. Our construction works for any choice of level. When K is simple and simply-connected, the level is just an integer as usual. For general K, the level is a bilinear form b on a Cartan subalgebra where b satisfies a qu...
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 Algebra
سال: 1996
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0151