Quaternion Algebras and the Algebraic Legacy of Hamilton's Quaternions

By David W. Lewis. Irish Mathematical Society Bulletin, 2006

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We describe the basic definitions and fundamen- tal properties of quaternion algebras over fields and proceed to give an account of how Hamilton's 1843 discovery of the quaternions was a major turning point in the subject of al- gebra. Noncommutative algebra started here! We will em- phasize especially the theory of division algebras and other kinds of algebras which emanated from this discovery.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

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