"Degrees and exponents"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 7번째 줄: | 7번째 줄: | ||
==Cartan matrix== | ==Cartan matrix== | ||
| − | * h : [[Coxeter number]]<br> | + | * h : [[Coxeter number and dual Coxeter number|Coxeter number]]<br> |
* eigenvalue<br><math>4\sin^2(\frac{m_{i}\pi}{2h})</math><br> | * eigenvalue<br><math>4\sin^2(\frac{m_{i}\pi}{2h})</math><br> | ||
* <math>m_{i}</math> is called the exponents<br> | * <math>m_{i}</math> is called the exponents<br> | ||
* <math>d_{i}=m_{i}+1</math> is called a degree<br> | * <math>d_{i}=m_{i}+1</math> is called a degree<br> | ||
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==adjacency matrix== | ==adjacency matrix== | ||
2012년 12월 17일 (월) 17:43 판
introduction
- eigenvalues of Cartan matrices
- eigenvalues of incidence matrices of Dynkin diagram
- http://pythagoras0.springnote.com/pages/1938682/attachments/3170605
Cartan matrix
- h : Coxeter number
- eigenvalue
\(4\sin^2(\frac{m_{i}\pi}{2h})\) - \(m_{i}\) is called the exponents
- \(d_{i}=m_{i}+1\) is called a degree
adjacency matrix
- h : Coxeter number
- eigenvalue \(2\cos(\pi l_n/h)\)
- Table[Simplify[2 Cos[Pi*l/5]], {l, 1, 4}]
Table[Simplify[4 Sin[Pi*l/10]^2], {l, 1, 4}]
homological algebraic characterization
For a s.s. Lie algebra L
(a)H'(L) is a free super- commutative algebra with homogeneous generator in degrees 2m_1+1,\cdots,2m_l+1
history
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Coxeter_number
- http://en.wikipedia.org/wiki/
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles
- 논문정리
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html[1]
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/