Abstract:
In this work we discuss groups of matrices and Differential equations in matrices via Quaternion's and Clifford algebras. Also we present a homogeneous space as manifolds and connectivity of manifolds with examples and applications. Also we describe some results on the structure of compact connected Lie groups, focusing on the important notation of a maximal torus which is central to the classification of simple compact connected Lie groups, with some results.
Also we discuss the Morse theory with some applications to the topology of Lie groups.
