Bài giảng về đại số Lie và nhóm Lie


Introduction to Lie Algebras and Lie Groups

Fall 2008

 

International Master Class

Institute of Mathematics

Vietnam Academy of Science and Technology


This course will cover the basic theory of Lie groups and Lie algebras. The prequisites include knowledge of linear algebra and group theory as covered by Algebra courses and basic notions of differential geometry (manifolds, vector fields,… etc).

TIME and PLACE

  • 13:30 – 16:00, Monday, Wednesday and Thursday at Lecture hall 301A, Building A5.

  • The first lecture will be held on Wednesday, October 29, 2008.

INSTRUCTOR

Professor Pierre Cartier, IHES

The best way to contact Professor P. Cartier is during the lecture or at his office (room 110, building A5)

CONTENTS

 

 

 

  • Introduction: Global and infinitesimal symmetris

  • Lie algebras: Basic definitions, enveloping algebra, Hopf lgebras, classical Lie algebras, Cartan subalgebras (roots and weights)

  • Lie groups: Classical Lie groups, Lie algebra of a Lie group, algebraic groups, maximal torus and Bruhat decomposition

  • Basic results about linear representations

  • A glimpse into modern developments: Quantum groups , Lie groupoids

TEXTBOOKS

 

 

 

  1. A. Kirillov Jr., Introduction to Lie Groups and Lie Algebras, Cambridge University Press, 2002

  2. N. Bourbaki, Lie groups and Lie algebras Chapter 1-3 ISBN 3-540-64242-0, Chapters 4-6 ISBN 3-540-42650-7, Chapters 7-9 ISBN 3-540-43405-4

  3. J. P. Serre, Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University, LNM 1500, Springer

  4. R. Carter et al., Lectures on Lie Groups and Lie Algebras, LMS Student Texts Series, 1995

  5. J. E. Humphreys, Introduction to Lie Algebras and Representaion theory, Springer 1978

Note: Almost all of these textbooks are available at the library of the Institute of Mathematics. Some of them are available electronically also.

FINAL EXAM

The final exam will be posted here.

P.S. Cái này mình copy trên trang của Viện Toán, bác nào rảnh thì đi nghe nhá!

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