منابع مشابه
Circles and Clifford Algebras
We study smooth maps from an open subset of a real projective space to a sphere such that all germs of straight lines go to germs of circles (or points). We give a construction of such maps based on representations of Clifford algebras. It provides a complete purely geometric description of Clifford algebras representations in terms of circles. We also describe a connection between our problem ...
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I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simplylaced compact Lie groups. 1 Clifford Algebras Let A be a...
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This essay will present a brief outline of the theory of Clifford algebras, together with a small amount of material about quadratic forms. I follow loosely the well known book Geometric algebra by Emil Artin, but with elegant modifications that I saw originally in some lecture notes by Raoul Bott, (dating from 1962), subsequently included in [Atiyah-Bott-Shapiro:1964]. In the first section, I’...
متن کاملClifford Algebras and Spinors ∗
Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [1] and includes historical notes and b...
متن کاملClifford Algebras and Their Representations
Introductory and historical remarks Clifford (1878) introduced his ‘geometric algebras’ as a generalization of Grassmann algebras, complex numbers and quaternions. Lipschitz (1886) was the first to define groups constructed from ‘Clifford numbers’ and use them to represent rotations in a Euclidean space. É. Cartan discovered representations of the Lie algebras son(C) and son(R), n > 2, that do ...
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ژورنال
عنوان ژورنال: Functional Analysis and Its Applications
سال: 2004
ISSN: 0016-2663
DOI: 10.1023/b:faia.0000024867.02438.e3