New Directions in Hopf Algebras
by S. Montgomery, H. Schneider
Publisher: Cambridge University Press 2002
Number of pages: 485
Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras, and other areas of physics and mathematics. The book gives a clear picture of the current trends in this active field, with a focus on what is likely to be important in future research.
Home page url
Download or read it online for free here:
(multiple PDF files)
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 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 Douglas Lundholm, Lars Svensson - arXiv
These are lecture notes for a course on the theory of Clifford algebras. The various applications include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.
by Eric G. Wagner - Wagner Mathematics
A text on universal algebra with a strong emphasis on applications and examples from computer science. The text introduces signatures, algebras, homomorphisms, initial algebras, free algebras, and illustrates them with interactive applications.