The Octonions by John Carlos Baez
About this book :-
This text offers a deep and accessible overview of the octonions, the most exotic and least familiar of the normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics.
Octonions are a kind of number. They're part of a short list of number systems where you can divide and where multiplication behaves nicely with size. There are only four such systems:
1. Real numbers (like 1, 2.5, -3, etc.)
2. Complex numbers (like 3 + 2i)
3. Quaternions (used in 3D rotations, discovered by Hamilton)
4. Octonions (more mysterious and harder to understand)
The text describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. It also touch upon their applications in quantum logic, special relativity and super symmetry. The text is s suitable for both mathematicians and physicists, as well as advanced students interested in abstract algebra, geometry, and theoretical physics.
Book Detail :-
Title:
The Octonions by John Carlos Baez
Publisher:
John Baez
Year:
2001
Pages:
56
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
John Carlos Baez
(born 1961) is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. His research area is Mathematical Physics and Category Theory. He use category theory to study networks and help researchers use them in scientific software, such as quickly adaptable models of infectious disease. He is also working on categorified ring theory, which sheds new light on topics such as Schur functors, plethysm, and the splitting principle. His research includes work on spin foams in loop quantum gravity. He also worked on applications of higher categories to physics, such as the cobordism hypothesis. He has also dedicated many efforts towards applied category theory, including network theory. He earned his doctorate in 1986 from the Massachusetts Institute of Technology under the direction of Irving Segal. Baez was a post-doctoral researcher at Yale University. Since 1989, he has been a faculty member at UC Riverside. From 2010 to 2012, he took a leave of absence to work at the Centre for Quantum Technologies in Singapore and has since worked there in the summers.
Book Contents :-
1. Introduction
2. Constructing the Octonions
3. Octonionic Projective Geometry
4. Exceptional Lie Algebras
5. Conclusions
6. Bibliography
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