Clifford algebra, geometric algebra, and applications
Authors: Douglas Lundholm, Lars Svensson
(Submitted on 30 Jul 2009)
Abstract: 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
(then called geometric algebra) 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. The various applications
presented include vector space and projective geometry, orthogonal
maps and spinors, normed division algebras, as well as simplicial
complexes and graph theory.
http://arxiv.org/abs/0907.5356
Geometric (Clifford) algebra and its applications
Authors: Douglas Lundholm
(Submitted on 10 May 2006)
Abstract: In this Master of Science Thesis I introduce geometric
algebra both from the traditional geometric setting of vector spaces,
and also from a more combinatorial view which simplifies common
relations and operations.
http://arxiv.org/abs/math/0605280