The Algebraic Theory of Spinors and Clifford Algebras: Collected WorksIn 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science. |
Contents
III | 5 |
V | 7 |
VI | 10 |
VII | 11 |
VIII | 13 |
IX | 18 |
X | 20 |
XI | 23 |
XXXIV | 86 |
XXXV | 101 |
XXXVI | 106 |
XXXVII | 113 |
XXXVIII | 119 |
XXXIX | 121 |
XL | 122 |
XLI | 124 |
XII | 27 |
XIII | 29 |
XIV | 31 |
XV | 35 |
XVI | 37 |
XVII | 38 |
XVIII | 43 |
XIX | 45 |
XX | 48 |
XXI | 52 |
XXII | 53 |
XXIII | 57 |
XXIV | 62 |
XXV | 67 |
XXVI | 69 |
XXVII | 70 |
XXIX | 72 |
XXX | 75 |
XXXI | 77 |
XXXII | 79 |
XXXIII | 83 |
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Common terms and phrases
antiautomorphism anticommutes antiderivation associated bilinear form Assume automorphism bilinear form characteristic Chevalley Clifford algebra Clifford group component of degree conjugate contains decomposable defined denote dimension Dirac operator direct sum elements of degree endomorphism equivalent extends exterior algebra follows immediately formula geometric graded algebra half-spin representations half-spinors homogeneous component homogeneous elements homogeneous of degree homomorphism ideal identity invariant isomorphism kernel leaves the elements Lemma linear mapping linearly independent M₁ maximal totally singular module morphism multiplication N₁ nondegenerate nonsingular vector octonions operation of G orthogonal group P₁ proof proves our assertion pure spinors quadratic form representation of G representative spinor restriction of Q scalar semi-graded sentation simple representations spin representation subalgebra tensor algebra tensor product Theorem totally singular space totally singular subspace u₁ vector space whence x₁ y₁ Z₁