Lie Groups and Lie Algebras I

Onishchik, A. L.; Vinberg, Ė. B.

doi:10.1007/978-3-642-57999-8

Cited by 117 publications

(2 citation statements)

References 74 publications

(130 reference statements)

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“…We were expecting that one of the group axioms of the multiplication in n  h not to be satisfied, since otherwise this manifold would be a Lie group and it is known (see [5], page 140) that every Lie group is an orientable manifold.…”

Section: Antianalytic Involutions Of N mentioning

confidence: 99%

Lie Groups Actions on Non Orientable <i>n</i>-Dimensional Complex Manifolds

Cao-Huu¹,

Ghişa²

2021

APM

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Analytic atlases on n can be easily defined making it an n-dimensional complex manifold. Then with the help of bi-Möbius transformations in complex coordinates Abelian groups are constructed making this manifold a Lie group. Actions of Lie groups on differentiable manifolds are well known and serve different purposes. We have introduced in previous works actions of Lie groups on non orientable Klein surfaces. The purpose of this work is to extend those studies to non orientable n-dimensional complex manifolds. Such manifolds are obtained by factorizing n  with the two elements group of a fixed point free antianalytic involution of n  . Involutions ( ) h z of this kind are obtained linearly by composing special Möbius transformations of the planes with the mapping ( ) 1. A convenient partition of n  is performed which helps defining an internal operation on n  h and finally actions of the previously defined Lie groups on the non orientable manifold n  h are displayed.

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Section: Antianalytic Involutions Of N mentioning

confidence: 99%

Lie Groups Actions on Non Orientable <i>n</i>-Dimensional Complex Manifolds

Cao-Huu¹,

Ghişa²

2021

APM

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“…In the list above (which is based on the one in [10]), and throughout the paper, r denotes the dimension of the Lie algebra. Our g 16 is by y → 1 y−x locally equivalent to ∂ x + ∂ y , x∂ x + y∂ y , x 2 ∂ x + y 2 ∂ y , which often appears in these lists of Lie algebras of vector fields on the plane but has a singular orbit y − x = 0.…”

Section: Classification Of Lie Algebra Actions On Cmentioning

confidence: 99%

Projectable Lie algebras of vector fields in 3D

Schneider

2018

Journal of Geometry and Physics

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Starting with Lie's classification of finite-dimensional transitive Lie algebras of vector fields on C 2 we construct Lie algebras of vector fields on the bundle C 2 × C by lifting the Lie algebras from the base. There are essentially three types of transitive lifts and we compute all of them for the Lie algebras from Lie's classification. The simplest type of lift is encoded by Lie algebra cohomology.

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