Exceptional Lie groups

Erscheinungsjahr 2025
ISBN: 978-3-031-88910-3
Verlag: Springer Nature Switzerland

Buch, Englisch, 252 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Yokota, Ichiro

Ishihara, Tetsuo

Imai, Takao

Mitsuishi, Kazuyuki

Yasukura, Osami

Miyashita, Toshikazu

Miyasaka, Takashi

Nishio, Akihiro

Shukuzawa, Osamu

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

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”.