**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

**Abstract Algebra: The Basic Graduate Year**

by

**Robert B. Ash**

Text for a graduate course in abstract algebra, it covers fundamental algebraic structures (groups, rings, fields, modules), and maps between them. The text is written in conventional style, the book can be used as a classroom text or as a reference.

(

**13195**views)

**Infinite-dimensional Lie Algebras**

by

**Iain Gordon**-

**University of Edinburgh**

Contents: Central extensions; Virasoro algebra; Heisenberg algebra; Enveloping algebras; Hands-on loop and affine algebras; Simple Lie algebras; Kac-Moody Lie algebras; Dynkin diagrams; Forms, Weyl groups and roots; Root spaces; Affine Lie algebras.

(

**7643**views)

**New Directions in Hopf Algebras**

by

**S. Montgomery, H. Schneider**-

**Cambridge University Press**

Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras, and other areas. The book gives a clear picture of the current trends, with a focus on what will be important in future research.

(

**7185**views)

**The Algebra of Invariants**

by

**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.

(

**5609**views)