**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

**Workbook in Higher Algebra**

by

**David Surowski**

A set of notes for a Higher Algebra course. It covers Group Theory, Field and Galois Theory, Elementary Factorization Theory, Dedekind Domains, Module Theory, Ring Structure Theory, Tensor Products, Zornâ€™s Lemma and some Applications.

(

**15290**views)

**A Course in Universal Algebra**

by

**S. Burris, H.P. Sankappanavar**-

**Springer-Verlag**

Selected topics in universal algebra: an introduction to lattices, the most general notions of universal algebra, a careful development of Boolean algebras, discriminator varieties, the introduction to the basic concepts and results of model theory.

(

**20384**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.

(

**8500**views)

**On Lie Algebras Of Prime Characteristic**

by

**George B. Seligman**-

**American Mathematical Society**

The purpose of the present memoir is to demonstrate the applicability, under certain restrictions on the algebra and the base field, of the techniques used in the determination of all simple Lie algebras of characteristic zero.

(

**4820**views)