Introduction to the Theory of Lie Groups

2017
ISBN: 978-3-319-54373-4
Verlag: Springer International Publishing

Buch, Englisch, 293 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 4628 g

Reihe: Universitext

This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory.

Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.

Zielgruppe

Graduate

Autoren/Hrsg.

Godement, Roger

Weitere Mitwirkende

Ray, Urmie

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Topological Groups.- Simply Connected Spaces and Groups.- Analytic Properties of Linear Groups.- Manifolds and Lie Group.- The Lie Algebra of a Lie Group.- The Exponential Map for Lie Groups.

Über Autor(innen)

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on abstract algebra and mathematical analysis.