Isometries and quaternions
Lecturer: Ruben Tellechea Zamanillo
Date: 08/03/2017
Time: 17:00
Place: Room 103
Abstract: It is known that the complex numbers appeared as an extension of $\mathbb{R}$ to find solutions to equations such as $x ^ 2 + 1 = 0$ . The field $\mathbb{C}$ can be extended again to $\mathbb{H}$ by adding another imaginary unit $j$ such that $j^2 = -1$. $\mathbb{H}$ is (as $\mathbb{C}$) a real division algebra algebraically closed. With the product of quaternions we can represent the isometries in the real three-dimensional euclidean vector space (R3) easily. In this colloquium we will present some concepts to understand better these representations and their utilities.
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Bibliography
- Verónica Pericacho, Cuaterniones y octoniones
- Richard Palais, The classification of real division algebras
- Samuel Eilenberg and Ivan Niven, The “fundamental theorem of algebra” for quaternions.
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