"History of Lie theory"의 두 판 사이의 차이
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imported>Pythagoras0 |
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http://mathoverflow.net/questions/87627/fraktur-symbols-for-lie-algebras-mathfrakg-etc | http://mathoverflow.net/questions/87627/fraktur-symbols-for-lie-algebras-mathfrakg-etc | ||
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development of representation theory of finite groups | development of representation theory of finite groups | ||
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| − | + | 1913 Cartan spin representations | |
19?? Weyl unitarian trick : complete reducibility | 19?? Weyl unitarian trick : complete reducibility | ||
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Dynkin, The structure of semi-simple Lie algebras | Dynkin, The structure of semi-simple Lie algebras | ||
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[http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_69-100.pdf From General Relativity to Group Representations] | [http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_69-100.pdf From General Relativity to Group Representations] | ||
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| − | + | ==19세기 프랑스 군론== | |
* 갈루아 | * 갈루아 | ||
* Jordan | * Jordan | ||
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| − | + | ==리 군== | |
* 클라인 | * 클라인 | ||
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* 카르탄 | * 카르탄 | ||
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| − | + | ==리 타입의 유한군== | |
* 딕슨 | * 딕슨 | ||
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* Chevalley 대수적 접근 | * Chevalley 대수적 접근 | ||
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| − | + | ==articles== | |
# Elie Cartan [http://books.google.com/books?id=JY8LAAAAYAAJ 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. | # Elie Cartan [http://books.google.com/books?id=JY8LAAAAYAAJ 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. | ||
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# Chevalley, On certain simple groups | # Chevalley, On certain simple groups | ||
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| − | + | ==표준적인 교과서== | |
* J.-P. Serre, [http://www.springerlink.com/content/v77q804n5808 Lie algebras and Lie groups] ISBN 978-3540550082 Covers most of the basic theory of Lie algebras. | * J.-P. Serre, [http://www.springerlink.com/content/v77q804n5808 Lie algebras and Lie groups] ISBN 978-3540550082 Covers most of the basic theory of Lie algebras. | ||
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* Claudio Procesi, [http://www.springerlink.com/content/978-0-387-26040-2 Lie Groups: An Approach through Invariants and Representations], ISBN 978-0387260402. Similar to the course, with more emphasis on invariant theory. | * Claudio Procesi, [http://www.springerlink.com/content/978-0-387-26040-2 Lie Groups: An Approach through Invariants and Representations], ISBN 978-0387260402. Similar to the course, with more emphasis on invariant theory. | ||
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| − | + | ==expository== | |
* T. Hawkins [http://books.google.com/books?isbn=978-0-387-98963-1 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. | * T. Hawkins [http://books.google.com/books?isbn=978-0-387-98963-1 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. | ||
2012년 10월 27일 (토) 15:26 판
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
- Jordan
리 군
- 클라인
- 리
- 킬링
- 카르탄
리 타입의 유한군
- 딕슨
- Tits 기하학적 접근
- Chevalley 대수적 접근
articles
- 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.
- 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.
- S. Lie, F. Engel "Theorie der transformationsgruppen" 1888 Volume 1Volume 2Volume 3 Lie's monumental summary of his work on Lie groups and algebras.
- 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.
- 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
- 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.