The Octonions
by John C. Baez
Publisher: University of California 2001
Number of pages: 56
Description:
The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.
Download or read it online for free here:
Download link
(420KB, PDF)
Similar books
An Invitation to General Algebra and Universal Constructionsby George M. Bergman - Henry Helson
From the contents: Free groups; Ordered sets, induction, and the Axiom of Choice; Lattices, closure operators, and Galois connections; Categories and functors; Universal constructions in category-theoretic terms; Varieties of algebras; etc.
(15327 views)
The Algebra of Invariantsby J.H. Grace, A. Young - Cambridge, University Press
Invariant theory is a subject within abstract algebra that studies polynomial functions which do not change under transformations from a linear group. This book provides an English introduction to the symbolical method in the theory of Invariants.
(12715 views)
Universal Algebra for Computer Scienceby Eric G. Wagner - Wagner Mathematics
A text on universal algebra with a strong emphasis on applications and examples from computer science. The text introduces signatures, algebras, homomorphisms, initial algebras, free algebras, and illustrates them with interactive applications.
(16790 views)
Lectures on Quadratic Formsby C.L. Siegel - Tata Institute of Fundamental Research
From the table of contents: Vector groups and linear inequalities (Vector groups, Lattices, Characters, Diophantine approximations); Reduction of positive quadratic forms; Indefinite quadratic forms; Analytic theory of Indefinite quadratic forms.
(12315 views)