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Lectures on exceptional Lie groups / J.F. Adams ; [edited by] Zafer Mahmud and Mamoru Mimura.

By: Contributor(s): Material type: TextTextSeries: Chicago lectures in mathematics seriesPublication details: Chicago : University of Chicago Press, c1996.Description: xiv, 122 p. : ill. ; 24 cmISBN:
  • 9780226005263 (cloth : alk. paper)
Subject(s): DDC classification:
  • 512.55 23 Ad214
Contents:
Ch. 1. Definitions, examples and matrix groups -- Ch. 2. Clifford algebras -- Ch. 3. The Spin groups -- Ch. 4. Clifford modules and representations -- Ch. 5. Applications of Spin representations -- Ch. 6. The exceptional groups: construction of E[subscript 8] -- Ch. 7. Construction of a Lie group of type E[subscript 8] -- Ch. 8. The construction of Lie groups of type F[subscript 4], E[subscript 6], E[subscript 7] -- Ch. 9. The Dynkin diagrams of F[subscript 4], E[subscript 6], E[subscript 7], E[subscript 8] -- Ch. 10. The Weyl group of E[subscript 8] -- Ch. 11. Representations of E[subscript 6], E[subscript 7] -- Ch. 12. Direct construction of E[subscript 7] -- Ch. 13. Direct treatment of E[subscript 6] -- Ch. 14. Direct treatment of F[subscript 4], I -- Ch. 15. The Cayley numbers -- Ch. 16. Direct treatment of F[subscript 4], II: Jordan algebras -- Appendix. Jordan algebras-- References.
Summary: J. Frank Adams was internationally known and respected as one of the great algebraic topologists. Adams had long been fascinated with exceptional Lie groups, about which he published several papers, and he gave a series of lectures on the topic. The author's detailed lecture notes have enabled volume editors Zafer Mahmud and Mamoru Mimura to preserve the substance and character of Adams's work. Because Lie groups form a staple of most mathematics graduate students' diets, this work on exceptional Lie groups should appeal to many of them, as well as to researchers of algebraic geometry and topology. J. Frank Adams was Lowndean professor of astronomy and geometry at the University of Cambridge. The University of Chicago Press published his Lectures on Lie Groups and has reprinted his Stable Homotopy and Generalized Homology. Chicago Lectures in Mathematics Series
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Includes bibliographical references ([121]-122).

Ch. 1. Definitions, examples and matrix groups --
Ch. 2. Clifford algebras --
Ch. 3. The Spin groups --
Ch. 4. Clifford modules and representations --
Ch. 5. Applications of Spin representations --
Ch. 6. The exceptional groups: construction of E[subscript 8] --
Ch. 7. Construction of a Lie group of type E[subscript 8] --
Ch. 8. The construction of Lie groups of type F[subscript 4], E[subscript 6], E[subscript 7] --
Ch. 9. The Dynkin diagrams of F[subscript 4], E[subscript 6], E[subscript 7], E[subscript 8] --
Ch. 10. The Weyl group of E[subscript 8] --
Ch. 11. Representations of E[subscript 6], E[subscript 7] --
Ch. 12. Direct construction of E[subscript 7] --
Ch. 13. Direct treatment of E[subscript 6] --
Ch. 14. Direct treatment of F[subscript 4], I --
Ch. 15. The Cayley numbers --
Ch. 16. Direct treatment of F[subscript 4], II: Jordan algebras --

Appendix. Jordan algebras--
References.

J. Frank Adams was internationally known and respected as one of the great algebraic topologists. Adams had long been fascinated with exceptional Lie groups, about which he published several papers, and he gave a series of lectures on the topic. The author's detailed lecture notes have enabled volume editors Zafer Mahmud and Mamoru Mimura to preserve the substance and character of Adams's work. Because Lie groups form a staple of most mathematics graduate students' diets, this work on exceptional Lie groups should appeal to many of them, as well as to researchers of algebraic geometry and topology. J. Frank Adams was Lowndean professor of astronomy and geometry at the University of Cambridge. The University of Chicago Press published his Lectures on Lie Groups and has reprinted his Stable Homotopy and Generalized Homology. Chicago Lectures in Mathematics Series

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