An Introduction to Lie Groups and the Geometry of by Arvanitogeorgos, Andreas

By Arvanitogeorgos, Andreas

It truly is amazing that loads approximately Lie teams can be packed into this small e-book. yet after examining it, scholars may be well-prepared to proceed with extra complicated, graduate-level subject matters in differential geometry or the speculation of Lie teams.

The idea of Lie teams contains many components of arithmetic: algebra, differential geometry, algebraic geometry, research, and differential equations. during this ebook, Arvanitoyeorgos outlines adequate of the must haves to get the reader began. He then chooses a course via this wealthy and numerous idea that goals for an figuring out of the geometry of Lie teams and homogeneous areas. during this method, he avoids the additional element wanted for an intensive dialogue of illustration idea.

Lie teams and homogeneous areas are specifically important to review in geometry, as they supply first-class examples the place amounts (such as curvature) are more straightforward to compute. a great knowing of them presents lasting instinct, in particular in differential geometry.

The writer offers numerous examples and computations. issues mentioned contain the class of compact and hooked up Lie teams, Lie algebras, geometrical facets of compact Lie teams and reductive homogeneous areas, and demanding periods of homogeneous areas, corresponding to symmetric areas and flag manifolds. purposes to extra complex themes also are integrated, similar to homogeneous Einstein metrics, Hamiltonian structures, and homogeneous geodesics in homogeneous areas.

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