Exceptional Lie groups
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Beschreibung
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.
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.
Describes the identity connected components of the real and complex exceptional Lie groups Adopts an elementary, concrete approach Does not require prior knowledge of composition algebras or Jordan algebras
Autor*in
Ichiro Yokota
Themen in »Exceptional Lie groups«
Exceptional Lie groups Identity connected component Elementary constructions Freudenthal constructions Jordan algebras Composition algebras
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“The book contains a lot of explicit calculations and is a wonderful reference book on the subject.” (Dmitry V. Artamonov, Mathematical Reviews, June, 2026)
“Each chapter follows a consistent structure ... . The presentation is algebraically rigorous yet elementary in spirit, avoiding reliance on general structural theory in favor of concrete constructions. This makes the volume a valuable resource for researchers seeking hands-on realizations of exceptional groups and their substructures, as well as for physicists interested in their symmetry properties, particularly in connection with grand unified theories and string-theoretic models. ” (Egle Bettio, zbMATH 1569.22002, 2026)
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