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 George B. Seligman - American Mathematical Society
The purpose of the present memoir is to demonstrate the applicability, under certain restrictions on the algebra and the base field, of the techniques used in the determination of all simple Lie algebras of characteristic zero.
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.
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.
by J.H. Grace, A. Young - Cambridge, University Press
Invariant theory is a subject within abstract algebra that studies polynomial functions which do not change under transformations from a linear group. This book provides an English introduction to the symbolical method in the theory of Invariants.