An Elementary Introduction to the Hopf Fibration
| Autor: | David W. Lyons |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Pure mathematics
Mathematics - History and Overview General Mathematics History and Overview (math.HO) 010102 general mathematics FOS: Physical sciences Mathematical Physics (math-ph) Quasitriangular Hopf algebra 01 natural sciences Algebra FOS: Mathematics 0101 mathematics Hopf fibration Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.2212.01642 |
| Popis: | The Hopf fibration is an important object in mathematics and physics. A landmark discovery in topology and a fundamental object in the theory of Lie groups, the Hopf fibration has a wide variety of physical applications including magnetic monopoles, rigid body mechanics, and quantum information theory. This expository article presents an introduction to the Hopf fibration that is accessible to undergraduate students. We use the algebra of quaternions to illustrate algebraic and geometric properties of the Hopf fibration and the connection with rotations of 3-space that is the basis for natural applications to physics and engineering. Comment: 17 pages, 11 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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