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The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G2, and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.
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This volume contains a facsimile reproduction of Marcel Riesz's notes of a set of lectures he delivered at the University of Maryland, College Park, between October 1957 and January 1958, which has not been formally published to date. This seminal material (arranged in four chapters), which contributed greatly to the start of modern research on Clifford algebras, is supplemented in this book by notes which Riesz dictated to E. Folke Bolinder in the following year and which were intended to be a fifth chapter of the Riesz lecture notes. In addition, Riesz's work on Clifford algebra is put into an historical perspective in a separate review by P. Lounesto. As well as providing an introduction to Clifford algebra, this volume will be of value to those interested in the history of mathematics.
Clifford algebras. --- Spinor analysis. --- Spinor analysis --- Clifford algebras
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