"Degrees and exponents"의 두 판 사이의 차이

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imported>Pythagoras0
imported>Pythagoras0
 
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==introduction==
 
==introduction==
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* {{수학노트|url=콕세터_군의_차수와_지수_(degrees_and_exponents)}}
  
*  eigenvalues of Cartan matrices<br>
 
*  eigenvalues of incidence matrices of Dynkin diagram<br>
 
* http://pythagoras0.springnote.com/pages/1938682/attachments/3170605
 
  
==Cartan matrix==
 
 
*  h : [[Coxeter number]]<br>
 
*  eigenvalue<br><math>4\sin^2(\frac{m_{i}\pi}{2h})</math><br>
 
* <math>m_{i}</math> is called the exponents<br>
 
* <math>d_{i}=m_{i}+1</math> is called a degree<br>
 
 
 
 
 
 
==adjacency matrix==
 
 
*  h : Coxeter number<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}]
 
 
 
 
 
 
==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==
 
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
 
 
 
 
  
 
==related items==
 
==related items==
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* [[Coxeter groups and reflection groups]]
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* [[Coxeter number and dual Coxeter number]]
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* [[Macdonald constant term conjecture]]
  
 
 
 
 
==encyclopedia==
 
 
* http://ko.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/Coxeter_number
 
* http://en.wikipedia.org/wiki/
 
 
 
 
 
 
 
==books==
 
 
 
 
* [[2010년 books and articles]]<br>
 
* http://gigapedia.info/1/
 
* http://gigapedia.info/1/
 
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
 
 
 
 
 
 
  
==articles==
 
  
 
  
* [[2010년 books and articles|논문정리]]
 
* http://www.ams.org/mathscinet
 
* http://www.zentralblatt-math.org/zmath/en/
 
* http://pythagoras0.springnote.com/
 
* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html][http://www.ams.org/mathscinet ]
 
* 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/
 
 
[[분류:개인노트]]
 
[[분류:개인노트]]
 
[[분류:Lie theory]]
 
[[분류:Lie theory]]
 
[[분류:math and physics]]
 
[[분류:math and physics]]
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[[분류:math]]
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[[분류:migrate]]

2020년 11월 13일 (금) 11:11 기준 최신판