Abstract
In this brief chapter we aim to lay the foundation for a formulation of the theory of Lie groups and Lie algebras in terms of Geometric Calculus. Such a reformulation of Lie theory appears to be desirable for several reasons. First, it is a step toward the unification of mathematics. Second, the coordinate-free methods of Geometric Calculus can be expected to simplify specific computations as well as the proofs of general results. Third, Geometric Algebra brings new methods and ideas to Lie theory which could simplify the theory and even lead to new results. Indeed, the structure of Geometric Algebra has so much in common with Lie algebra that we would be surprised if they could not be unified in a productive way.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Hestenes, D., Sobczyk, G. (1987). Lie Groups and Lie Algebras. In: Clifford Algebra to Geometric Calculus. Fundamental Theories of Physics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6292-7_8
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DOI: https://doi.org/10.1007/978-94-009-6292-7_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-2561-5
Online ISBN: 978-94-009-6292-7
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