Lie Algebras, Lie Groups, and Algebra of Incidence

Abstract

We have learned that readers of the work of D. Hestenes and G. Sobzyk (Hestenes and Sobczyk (1984). Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics.) [138] Chap. 8 and a late article of Ch. Doran, D. Hestenes and F. Sommen (Doran, Hestenes, Sommen and Van Acker (1993). Journal of Mathematical Physics, 34(8), pp. 3642–3669.) [72] Sect. IV may have difficulties to understand the subject and practitioners have difficulties to try the equations in certain applications. For this reason, this chapter reviews concepts and equations most of them introduced by D.Hestenes and G. Sobzyk (Hestenes and Sobczyk (1984). Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics.) [138] Chap. 8 and the article of Ch. Doran, D. Hestenes and F. Sommen (Doran, Hestenes, Sommen and Van Acker (1993). Journal of Mathematical Physics, 34(8), pp. 3642–3669.) [72] Sect. IV. This chapter is written in a clear manner for readers interested in applications in computer science and engineering. The explained equations will be required to understand advanced applications in next chapters.