In 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.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Editions-Typ
Illustrationen
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-540-57063-9 (9783540570639)
DOI
10.1007/978-3-642-60934-3
Schweitzer Klassifikation
Content.- The Construction And Studyof Certain Important Algebras.- I. Graded Algebras.- 1. Free Algebras.- 2. Graded Algebras.- 3. Homogeneous Linear Mappings.- 4. Associated Gradations and the Main Involution.- 5. Derivations.- 6. Existence of Derivations in Free Algebras.- II. Tensor Algebras.- 1. Tensor Algebras.- 2. Graded Structure of Tensor Algebras.- 3. Derivations in a Tensor Algebra.- 4. Preliminaries About Tensor Product of Modules.- 5.Tensor Product of Semi-Graded Algebras.- III. Clifford Algebras.- 1. Clifford Algebras.- 2. Exterior Algebras.- 3. Structure of the Clifford Algebra when M has a Base.- 4. Canonical Anti-Automorphism.- 5. Derivations in the Exterior Algebras; Trace.- 6. Orthogonal Groups and Spinors (a Review).- IV. Some Applications Of Exterior Algebras.- 1. Plücker Coordinates.- 2. Exponential Mapping.- 3. Determinants.- 4. An application to Combinatorial Topology.- The Algebraic Theory Of Spinors.- Preliminaries.- 1. Terminology.- 2. Associative Algebras.- 3. Exterior Algebras.- I. Quadratic Forms.- 1.1. Bilinear Forms.- 1.2. Quadratic Forms.- 1.3. Special Bases.- 1.4. The Orthogonal Group.- 1.5. Symmetries.- 1.6. Representation of G on the Multivectors.- II. The Clifford Algebra.- 2.1. Definition of the Clifford Algebra.- 2.2. Structure of the Clifford Algebra.- 2.3. The Group of Clifford.- 2.4. Spinors (Even Dimension).- 2.5. Spinors (Odd Dimension).- 2.6. Imbedded Spaces.- 2.7. Extension of the Basic Field.- 2.8. The Theorem of Hurwitz.- 2.9. Quadratic Forms over the Real Numbers.- III. Forms Of Maximal Index.- 3.1. Pure Spinors.- 3.2. A Bilinear Invariant.- 3.3. The Tensor Product of the Spin Representation with Itself.- 3.4. The Tensor Product of the Spin Representation with Itself (Characteristic ? 2).- 3.5. Imbedded Spaces.- 3.6. The Kernels of the Half-Spin Representations.- 3.7. The Case m = 6.- 3.8. The Case of Odd Dimension.- IV. The Principle Of Triality.- 4.1. A New Characterization of Pure Spinors.- 4.2. Construction of an Algebra.- 4.3. The Principle of Thiality.- 4.4. Geometric Interpretation.- 4.5. The Octonions.- Book Review.- Spinors In 1995.- Symbol Index.
