History of Lie theory

http://mathoverflow.net/questions/87627/fraktur-symbols-for-lie-algebras-mathfrakg-etc

 

development of representation theory of finite groups

 

1913  Cartan spin representations

19?? Weyl unitarian trick : complete reducibility

 

Dynkin, The structure of semi-simple Lie algebras

amre,math.sco.transl.17

history of theory of symmetric polynomials

From General Relativity to Group Representations

 

19세기 프랑스 군론

• 갈루아
• 조던

 

리 군

• 클라인
• 리
•  

 

리 타입의 유한군

• 딕슨
• Tits 기하학적 접근
• Chevalley 대수적 접근

 

 

articles

1. Elie Cartan Sur la structure des groupes de transformations finis et continus Cartan's famous 1894 thesis, cleaning up Killing's work on the classification Lie algebras.
2. Wilhelm Killing, "Die Zusammensetzung der stetigen endlichen Transformations-gruppen" 1888-1890 part 1part 2part 3part 4 Killing's classification of simple Lie complex Lie algebras.
3. S. Lie, F. Engel "Theorie der transformationsgruppen" 1888 Volume 1Volume 2Volume 3 Lie's monumental summary of his work on Lie groups and algebras.
4. Hermann Weyl, Theorie der Darstellung kontinuierlicher halb-einfacher Gruppen durch lineare Transformationen. 1925-1926 I, II, III. Weyl's paper on the representations of compact Lie groups, giving the Weyl character formula.
5. H. Weyl The classical groups ISBN 978-0-691-05756-9 A classic, describing the representation theory of lie groups and its relation to invariant theory
6. Chevalley, On certain simple groups

 

 

표준적인 교과서

• J.-P. Serre, Lie algebras and Lie groups ISBN 978-3540550082 Covers most of the basic theory of Lie algebras.
• J.-P. Serre, Complex semisimple Lie algebras ISBN 978-3-540-67827-4 Covers the classification and representation theory of complex Lie algebras.
• N. Jacobson, Lie algebras ISBN 978-0486638324 A good reference for all proofs about finite dimensional Lie algebras
• Claudio Procesi, Lie Groups: An Approach through Invariants and Representations, ISBN 978-0387260402. Similar to the course, with more emphasis on invariant theory.

 

 

expository

• T. Hawkins Emergence of the theory of Lie groups ISBN 978-0-387-98963-1 Covers the early history of the work by Lie, Killing, Cartan and Weyl, from 1868 to 1926.
• A. Borel Essays in the history of Lie groups and algebraic groups ISBN 978-0-8218-0288-5 Covers the history.
• "From Galois and Lie to Tits Buildings", The Coxeter Legacy: Reflections and Projections (ed. C. Davis and E.W. Ellers), Fields Inst. Publications volume 48, American Math. Soc. (2006), 45–62.
  
  • http://www.fields.utoronto.ca/programs/scientific/03-04/coxeterlegacy/abstracts.html