Tangent and Cotangent Bundles, and Representations of Lie Groups

Tangent and Cotangent Bundles, and Representations of Lie Groups

Firas Hindeleh

     

бумажная книга



Издательство: Книга по требованию
Дата выхода: июль 2011
ISBN: 978-3-6391-6634-7
Объём: 104 страниц
Масса: 178 г
Размеры(В x Ш x Т), см: 23 x 16 x 1

The European Union has tried to use innovative practices to foment good relations with borderland countries since the 1990s. Nevertheless, the success of the EU's framework policies can be questioned in view of the relative disinterest or reluctance which countries close to the Union's borders have displayed. This work wil try to explain the policies' failure to draw partners closer by exploring how the EU constructs and acts out its foreign policy identity vis-a-vis neighboring candidate and non-candidate countries. We will use the Barcelona Process/Union for the Mediterranean, the Northern Dimension and the Stabilization and Association process for Western Balkans to examine how the EU post-power identitarian projection creates contradictions and/or dissonance with non- member neighboring countries and to illustrate why the EU policies have not met with the expectations they generated at their inception.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

We study the tangent and cotangent bundles of a Lie group G which are also Lie groups. Our main results are to show that on TG the canonical Jacobi endomorphism field S is parallel with respect to the canonical Lie group connection Lie group and that dually on the cotangent bundle of G the canonical symplectic form is parallel with respect to the canonical connection. We next prove some theorems for Lie algebra extensions in which we can obtain a group representation for the extended algebra from the representation of the lower dimensional algebra. We also determine the Lie algebra of the automorphism group of three well known Lie algebras. Finally we study the Hamilton-Jacobi separability of conformally flat metrics and find a metric, Lagrangian and geodesics for the solvable codimension one nilradical six dimensional Lie Algebras where one exists.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.