Algebra, Lie Group and Lie Algebra

Daizhan Cheng (), Xiaoming Hu () and Tielong Shen ()
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Daizhan Cheng: Chinese Academy of Sciences, Academy of Mathematics & Systems Science
Xiaoming Hu: Royal Institute of Technology, Optimization and Systems Theory
Tielong Shen: Sophia University, Department of Engineering and Applied Sciences

Chapter Chapter 4 in Analysis and Design of Nonlinear Control Systems, 2010, pp 91-119 from Springer

Abstract: Abstract Geometry, algebra, and analysis are usually called the three main branches of mathematics. This chapter introduces some fundamental results in algebra that are mostly useful in systems and control. In section 4.1 some basic concepts of group and three homomorphism theorems are discussed. Ring and algebra are introduced briefly in section 4.2. As a tool, homotopy is investigated in section 4.3. Sections 4.4 and 4.5 contain some primary knowledge about algebraic topology, such as fundamental group, covering space etc. In sections 4.6 and 4.7, Lie group and its Lie algebra are discussed. Section 4.8 considers the structure of Lie algebra.

Keywords: Topological Space; Base Point; Fundamental Group; Covering Space; Basic Neighborhood (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11550-9_4

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