"Degrees and exponents"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
| − | + | ==introduction== | |
* eigenvalues of Cartan matrices<br> | * eigenvalues of Cartan matrices<br> | ||
* eigenvalues of incidence matrices of Dynkin diagram<br> | * eigenvalues of incidence matrices of Dynkin diagram<br> | ||
| − | + | ||
[http://pythagoras0.springnote.com/pages/1938682/attachments/3170605 ] | [http://pythagoras0.springnote.com/pages/1938682/attachments/3170605 ] | ||
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| − | + | ||
| − | + | ==Cartan matrix== | |
* h : [[Coxeter number]]<br> | * h : [[Coxeter number]]<br> | ||
| 19번째 줄: | 19번째 줄: | ||
* <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== | |
* h : Coxeter number<br> | * h : Coxeter number<br> | ||
* eigenvalue <math>2\cos(\pi l_n/h)</math><br> | * eigenvalue <math>2\cos(\pi l_n/h)</math><br> | ||
| − | + | ||
# Table[Simplify[2 Cos[Pi*l/5]], {l, 1, 4}]<br> Table[Simplify[4 Sin[Pi*l/10]^2], {l, 1, 4}] | # Table[Simplify[2 Cos[Pi*l/5]], {l, 1, 4}]<br> Table[Simplify[4 Sin[Pi*l/10]^2], {l, 1, 4}] | ||
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| − | + | ==homological algebraic characterization== | |
For a s.s. Lie algebra L | For a s.s. Lie algebra L | ||
| 42번째 줄: | 42번째 줄: | ||
(a)H'(L) is a free super- commutative algebra with homogeneous generator in degrees 2m_1+1,\cdots,2m_l+1 | (a)H'(L) is a free super- commutative algebra with homogeneous generator in degrees 2m_1+1,\cdots,2m_l+1 | ||
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| − | + | ||
| − | + | ==history== | |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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| − | + | ==related items== | |
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| − | + | ==encyclopedia== | |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 71번째 줄: | 71번째 줄: | ||
* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]]) | * Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]]) | ||
| − | + | ||
| − | + | ||
| − | + | ==books== | |
| − | + | ||
* [[2010년 books and articles]]<br> | * [[2010년 books and articles]]<br> | ||
| 84번째 줄: | 84번째 줄: | ||
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | * http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | ||
| − | [[4909919|]] | + | [[4909919|4909919]] |
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| − | + | ||
| − | + | ==articles== | |
| − | + | ||
* [[2010년 books and articles|논문정리]] | * [[2010년 books and articles|논문정리]] | ||
2012년 10월 27일 (토) 14:47 판
introduction
- eigenvalues of Cartan matrices
- eigenvalues of incidence matrices of Dynkin diagram
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/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
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[2]
- 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/