Search results
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 geomet-
Cli ord algebras are a a generalization of the complex numbers that have important uses in mathematical physics. We begin with an introduction to real Cli ord algebras and the connection to normed division algebras and braids.
Clifford algebras 1. Exterior algebras L 1.1. Definition. For any vector space V over a field K, let T(V) = k∈Z T k(V) be the tensor algebra, with Tk(V) = V⊗ ··· ⊗ V the k-fold tensor product. The quotient of T(V) by the two-sided ideal I(V) generated by all v⊗w+w⊗vis the exterior algebra, denoted ∧(V). The product in
This article reviews Clifford algebras, the associated groups and their representations, for quadratic spaces over complex or real numbers. These notions have been generalized by
Clifford algebras and Lie groups Eckhard Meinrenken Lecture Notes, University of Toronto, Fall 2009. (Revised version of lecture notes from 2005)
Clifford algebras and spin groups. Cli ord algebras were discovered by Cli ord in the late 19th century as part of his search for generalizations of quaternions. He considered an algebra generated by V = Rn subject to the relation v2 = jj vjj2 for all v 2 V . (For n = 2 this gives the quaternions via i = e1, j = e2, and k = e1e2.)
Clifford algebras and spinors. Bill Casselman University of British Columbia. cass@math.ubc.ca. This essay will present a brief outline of the theory of Clifford algebras, together with a small amount of material about quadratic forms.
