"History of Lie theory"의 두 판 사이의 차이
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# 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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# Wilhelm Killing, "Die Zusammensetzung der stetigen endlichen Transformations-gruppen" 1888-1890 [http://www.springerlink.com/content/g8010v1431329811/ part 1][http://www.springerlink.com/content/r5353067l8842662/ part 2][http://www.springerlink.com/content/l53068g50gx44p67/ part 3][http://www.springerlink.com/content/r2mu07227763325n/ part 4] Killing's classification of simple Lie complex Lie algebras. | # Wilhelm Killing, "Die Zusammensetzung der stetigen endlichen Transformations-gruppen" 1888-1890 [http://www.springerlink.com/content/g8010v1431329811/ part 1][http://www.springerlink.com/content/r5353067l8842662/ part 2][http://www.springerlink.com/content/l53068g50gx44p67/ part 3][http://www.springerlink.com/content/r2mu07227763325n/ part 4] Killing's classification of simple Lie complex Lie algebras. | ||
# S. Lie, F. Engel "Theorie der transformationsgruppen" 1888 [http://www.archive.org/details/theotransformation01liesrich Volume 1][http://www.archive.org/details/theoriedertrans01liegoog Volume 2][http://www.archive.org/details//theoriedertrans00liegoog Volume 3] Lie's monumental summary of his work on Lie groups and algebras. | # S. Lie, F. Engel "Theorie der transformationsgruppen" 1888 [http://www.archive.org/details/theotransformation01liesrich Volume 1][http://www.archive.org/details/theoriedertrans01liegoog Volume 2][http://www.archive.org/details//theoriedertrans00liegoog Volume 3] Lie's monumental summary of his work on Lie groups and algebras. | ||
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# Hermann Weyl, Theorie der Darstellung kontinuierlicher halb-einfacher Gruppen durch lineare Transformationen. 1925-1926 [http://dx.doi.org/10.1007/BF01506234 I], [http://dx.doi.org/10.1007/BF01216788 II], [http://dx.doi.org/10.1007/BF01216789 III]. Weyl's paper on the representations of compact Lie groups, giving the Weyl character formula. | # Hermann Weyl, Theorie der Darstellung kontinuierlicher halb-einfacher Gruppen durch lineare Transformationen. 1925-1926 [http://dx.doi.org/10.1007/BF01506234 I], [http://dx.doi.org/10.1007/BF01216788 II], [http://dx.doi.org/10.1007/BF01216789 III]. Weyl's paper on the representations of compact Lie groups, giving the Weyl character formula. | ||
# H. Weyl [http://books.google.com/books?isbn=978-0-691-05756-9 The classical groups] ISBN 978-0-691-05756-9 A classic, describing the representation theory of lie groups and its relation to invariant theory | # H. Weyl [http://books.google.com/books?isbn=978-0-691-05756-9 The classical groups] ISBN 978-0-691-05756-9 A classic, describing the representation theory of lie groups and its relation to invariant theory | ||
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| − | <h5> </h5> | + | <h5>표준적인 교과서</h5> |
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| + | * 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://books.google.com/books?isbn=978-3-540-67827-4 Complex semisimple Lie algebras] ISBN 978-3-540-67827-4 Covers the classification and representation theory of complex Lie algebras. | ||
| + | * N. Jacobson, [http://books.google.com/books?isbn=978-0486638324 Lie algebras] ISBN 978-0486638324 A good reference for all proofs about finite dimensional Lie algebras | ||
| + | * 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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| + | <h5>expository</h5> | ||
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| + | * 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. | ||
| + | * A. Borel [http://books.google.com/books?isbn=978-0-8218-0288-5 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. | ||
"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. | "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. | ||
2012년 8월 15일 (수) 09:00 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
original works
- 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
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.
"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.