"Degrees and exponents"의 두 판 사이의 차이

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# 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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2012년 8월 26일 (일) 11:07 판

introduction
  • eigenvalues of Cartan matrices
  • eigenvalues of incidence matrices of Dynkin diagram

 

[1]

 

 

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 \(2\cos(\pi l_n/h)\)

 

  1. 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

 

 

related items

 

 

encyclopedia

 

 

books

 

[[4909919|]]

 

 

articles

 

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