Abstract
Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three-dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.
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(left) Govind Krishnaswami is on the faculty of the Chennai Mathematical Institute. His research in theoretical physics spans various topics from quantum field theory and particle physics to fluid, plasma and non-linear dynamics.
(right) Sonakshi Sachdev is a PhD student at the Chennai Mathematical Institute. She has worked on the dynamics of rigid bodies, fluids and plasmas.
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Krishnaswami, G.S., Sachdev, S. Algebra and geometry of Hamilton’s quaternions. Reson 21, 529–544 (2016). https://doi.org/10.1007/s12045-016-0358-9
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DOI: https://doi.org/10.1007/s12045-016-0358-9