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* [http://www.google.com/url?sa=t&source=web&cd=1&ved=0CBsQFjAA&url=http%3A%2F%2Fmath.ucr.edu%2Fhome%2Fbaez%2Fhazewinkel_et_al.pdf&ei=kLRtTLHABYX0tgOa1IiTCw&usg=AFQjCNGkaQYcDIKOcDcuE0CTLcg-beS5-g&sig2=5v5TDImhd94YoZ6UjS4LPg The ubiquity of Coxeter Dynkin diagrams]<br> | * [http://www.google.com/url?sa=t&source=web&cd=1&ved=0CBsQFjAA&url=http%3A%2F%2Fmath.ucr.edu%2Fhome%2Fbaez%2Fhazewinkel_et_al.pdf&ei=kLRtTLHABYX0tgOa1IiTCw&usg=AFQjCNGkaQYcDIKOcDcuE0CTLcg-beS5-g&sig2=5v5TDImhd94YoZ6UjS4LPg The ubiquity of Coxeter Dynkin diagrams]<br> | ||
** Hazewinkel, M.; Hesseling, W.; Siersma, D.; Veldkamp, F., 1977-01-01 | ** Hazewinkel, M.; Hesseling, W.; Siersma, D.; Veldkamp, F., 1977-01-01 | ||
| + | * McKay, J. (1980). "Graphs singularities and finite groups". Proc. of 1979 Santa Cruz group theory conference. AMS Symposia in Pure Mathematics. 37. pp. 183–186. | ||
| + | * McKay, J. (1981). "Cartan matrices, finite groups of quaternions, and Kleinian singularities". Proc. AMS 81: 153–154. doi:10.1090/S0002-9939-1981-0589160-8. | ||
2012년 9월 18일 (화) 21:59 판
개요
- ADE는 원래 semisimple 리대수의 분류에서 사용되었음.
- 하지만 ADE 분류는 수학의 많은 분야에서 모습을 드러냄.
- 리군, 리대수, 루트 시스템, 딘킨 다이어그램, reflection 군, 정다면체, 곡면의 특이점 분류, quiver의 표현론 등
- 정다면체의 분류
- A - 피라미드
- D - 쌍피라미드(dipyramid)
- E6 - 정사면체, E7 - 정육면체, 정팔면체, E8 - 정십이면체,정이십면체
메모
- A Rapid Introduction to ADE Theory, John McKay
- The ADE affair
- http://cameroncounts.wordpress.com/2011/06/10/the-ade-affair-1/
- http://cameroncounts.wordpress.com/2011/06/14/the-ade-affair-2/
- http://cameroncounts.wordpress.com/2011/06/23/the-ade-affair-3/
- http://cameroncounts.wordpress.com/2011/07/03/the-ade-affair-4/
- http://cameroncounts.wordpress.com/2011/08/14/the-ade-affair-5/
하위주제들
- Finite reflection groups and Coxeter groups
- Regular polytopes
- 딘킨 다이어그램의 분류
- Classification of finite subgroups of SO(3) and SU(2)
- E8
관련된 항목들
관련논문
- E6, E7, E8
- Nigel Hitchin, Clay Mathematics Institute, 2005 Academy Colloquium Series
- The ubiquity of Coxeter Dynkin diagrams
- Hazewinkel, M.; Hesseling, W.; Siersma, D.; Veldkamp, F., 1977-01-01
- McKay, J. (1980). "Graphs singularities and finite groups". Proc. of 1979 Santa Cruz group theory conference. AMS Symposia in Pure Mathematics. 37. pp. 183–186.
- McKay, J. (1981). "Cartan matrices, finite groups of quaternions, and Kleinian singularities". Proc. AMS 81: 153–154. doi:10.1090/S0002-9939-1981-0589160-8.