by John C. Baez
Publisher: University of California 2001
Number of pages: 56
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.
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by G.H.E. Duchamp, et al. - arXiv
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics.
by W. B. Vasantha Kandasamy - American Research Press
The purpose of this book entirely lies in the study, introduction and examination of the Smarandache loops. We expect the reader to have a good background in algebra and more specifically a strong foundation in loops and number theory.
by D. Rogalski - arXiv
These lecture notes are an expanded version of the author's lectures at a graduate workshop. The main topics discussed are Artin-Schelter regular algebras, point modules, and the noncommutative projective scheme associated to a graded algebra.
by Michael Artin
From the table of contents: Morita equivalence (Hom, Bimodules, Projective modules ...); Localization and Goldie's theorem; Central simple algebras and the Brauer group; Maximal orders; Irreducible representations; Growth of algebras.