**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

**Universal Algebra for Computer Science**

by

**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.

(

**13258**views)

**An Introduction to Nonassociative Algebras**

by

**Richard D. Schafer**-

**Project Gutenberg**

Concise study presents in a short space some of the important ideas and results in the theory of nonassociative algebras, with particular emphasis on alternative and (commutative) Jordan algebras. Written as an introduction for graduate students.

(

**11350**views)

**Smarandache Rings**

by

**W. B. Vasantha Kandasamy**-

**American Research Press**

The author embarked on writing this book on Smarandache rings (S-rings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several important and innovative properties about S-rings.

(

**10402**views)

**Hopf Algebras in General and in Combinatorial Physics: a practical introduction**

by

**G.H.E. Duchamp, et al.**-

**arXiv**

This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics.

(

**7536**views)