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
Lectures on Quadratic Forms
by 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.
(12242 views)
by 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.
(12242 views)
The Construction and Study of Certain Important Algebras
by Claude Chevalley - The Mathematical Society Of Japan
This is the reproduction of the beautiful lectures delivered by Professor C. Chevalley at the University of Tokyo in April-June 1954. Contents: Graded algebras; Tensor algebras; Clifford algebras; Some applications of exterior algebras.
(11015 views)
by Claude Chevalley - The Mathematical Society Of Japan
This is the reproduction of the beautiful lectures delivered by Professor C. Chevalley at the University of Tokyo in April-June 1954. Contents: Graded algebras; Tensor algebras; Clifford algebras; Some applications of exterior algebras.
(11015 views)
Hopf Algebras, Quantum Groups and Yang-Baxter Equations
by Florin Felix Nichita (ed.) - MDPI AG
Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are presented. The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed.
(6942 views)
by Florin Felix Nichita (ed.) - MDPI AG
Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are presented. The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed.
(6942 views)
A Treatise on the Theory of Invariants
by Oliver E. Glenn - Project Gutenberg
The object of this book is to present in a volume of medium size the fundamental principles and processes and a few of the multitudinous applications of invariant theory, with emphasis upon both the nonsymbolical and the symbolical method.
(12202 views)
by Oliver E. Glenn - Project Gutenberg
The object of this book is to present in a volume of medium size the fundamental principles and processes and a few of the multitudinous applications of invariant theory, with emphasis upon both the nonsymbolical and the symbolical method.
(12202 views)