A Study Of Lie Algebra Including Exponential Maps, Adjoint Representations, Killing Form, And Lie Point Symmetry

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie grou... Read more

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.

In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra," after Sophus Lie, was introduced by Hermann Weyl in the 1930s. Every finite-dimensional, real, or complex Lie algebra has a faithful representation by matrices. Lie's fundamental theorems describe a relation between Lie groups and Lie algebras. In particular, any Lie group gives rise to a canonically determined Lie algebra and conversely, for any Lie algebra there is a corresponding connected Lie group. This book studies Lie algebra including exponential function, group action, symmetric bilinear form, and discrete symmetry.

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