**Memoires de la Societe Mathematique de France**

Volume: 151;
2017;
147 pp;
Softcover

MSC: Primary 17;
**Print ISBN: 978-2-85629-859-6
Product Code: SMFMEM/151**

List Price: $52.00

Individual Member Price: $41.60

# Semisimple Lie Algebras and Their Classification Over \(p\)-Adic Fields

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*Torsten Schoeneberg*

A publication of the Société Mathématique de France

This book gives a detailed structure theory for semisimple
Lie algebras over arbitrary fields of characteristic 0. Starting from
the well-known classification over algebraically closed fields via
root systems, the author mimics the language of reductive groups, so that part
of his work can be seen as an introduction to a simpler version of
Borel-Tits theory. But the author also expresses his results in the language of
classical (matrix) algebra as well as Galois cohomology.

In the second part of this book, the author focuses on
\(p\)-adic fields and achieves a complete classification of
semisimple Lie algebras over them. This classification consists
essentially of a list of so-called Satake-Tits diagrams, which extend
the Dynkin diagrams from the split case. Several instructive examples
and historical notes supplement the text. This book can be used as the
basis for a lecture on semisimple Lie algebras beyond the beginner's
level and as a reference for researchers.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students, research mathematicians, and historians of mathematics.