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Algebra, Lie Group and Lie Algebra

In: Analysis and Design of Nonlinear Control Systems

Author

Listed:
  • 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)

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.

Suggested Citation

  • Daizhan Cheng & Xiaoming Hu & Tielong Shen, 2010. "Algebra, Lie Group and Lie Algebra," Springer Books, in: Analysis and Design of Nonlinear Control Systems, chapter 0, pages 91-119, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11550-9_4
    DOI: 10.1007/978-3-642-11550-9_4
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