Exceptional Lie groups
Springer International Publishing (Verlag)
978-3-031-88910-3 (ISBN)
This book provides a concrete description of the identity connected components of the real and complex exceptional Lie groups. The constructions are elementary and improve on those of H. Freudenthal.
The complex simple Lie algebras were classified into classical (An, Bn, Cn, Dn) and exceptional (G2, F4, E6, E7, E8) types at the end of the 19th century by W. Killing and É. Cartan. These simple Lie algebras and the corresponding compact simple Lie groups arise in many settings in mathematics and physics. The exceptional Lie groups form an especially interesting class of objects that have attracted the attention of numerous mathematicians. Requiring no prior knowledge of composition algebras or Jordan algebras, the book will be valuable to anyone who wants to learn about the structure and realizations of these fascinating groups.
Ichiro Yokota was awarded a Doctor of Science degree (Topology of classical Lie groups) from Osaka University in 1959. He was an Assistant, Lecturer and then Associate Professor at Osaka City University (1950 1966), Professor at Shinshu University (1966 1990) and Visiting Professor at Tamkang University (1976 1977). In 1990, he became a Professor Emeritus at Shinshu University. With O. Shukuzawa, he realized the non-compact connected and compact simply connected exceptional Lie groups of type E6 (1979 1980), improving on H. Freudenthal s constructions. His publications include the book "Groups and Topology (Shokabo, 1971) on cellular decompositions of classical Lie groups. Professor Yokota died on November 10th, 2017. The editors of this book have been disciples of the late Professor since 1976. In his words, Our motivation is to study everything related to exceptional Lie groups .
Chapter 1. Exceptional Lie group G2.- Chapter 2. Exceptional Lie group F4.- Chapter 3. Exceptional Lie group E6.- Chapter 4. Exceptional Lie group E7.- Chapter 5. Exceptional Lie group E8.
| Erscheinungsdatum | 31.05.2025 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | XIX, 252 p. 7 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | composition algebras • Elementary constructions • Exceptional Lie groups • Freudenthal constructions • Identity connected component • Jordan Algebras |
| ISBN-10 | 3-031-88910-X / 303188910X |
| ISBN-13 | 978-3-031-88910-3 / 9783031889103 |
| Zustand | Neuware |
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