Clifford Algebra, Geometric Algebra, and Applications
by Douglas Lundholm, Lars Svensson
Publisher: arXiv 2009
Number of pages: 117
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction with geometric applications in mind, as well as in an algebraically more general form which is well suited for combinatorics, and for defining and understanding the numerous products and operations of the algebra.
Home page url
Download or read it online for free here:
by Leonard Evens - Northwestern University
Contents: Groups; Group actions on sets; Normal series; Ring theory; Modules; Hom and tensor; Field theory; Galois theory; Applications of Galois theory; Infinite extensions; Categories; Multilinear algebra; More ring theory; Localization; etc.
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.
by John C. Baez - University of California
The octonions are the largest of the four normed division algebras. The author describes them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups.
by W. B. Vasantha Kandasamy - American Research Press
Near-rings are one of the generalized structures of rings. This is a book on Smarandache near-rings where the Smarandache analogues of the near-ring concepts are developed. The reader is expected to have a background in algebra and in near-rings.