Braid group

review of symmetric groups

• 원소의 개수가 n인 집합의 전단사함수들의 모임
• \(n!\) 개의 원소가 존재함
• 대칭군의 부분군은 치환군(permutation group)이라 불림

 

 

presentation of symmetric groups

• 생성원 \(\sigma_1, \ldots, \sigma_{n-1}\)
  
• relations
  
  • \({\sigma_i}^2 = 1\)
    
  • \(\sigma_i\sigma_j = \sigma_j\sigma_i \mbox{ if } j \neq i\pm 1\)
    
  • \(\sigma_i\sigma_{i+1}\sigma_i = \sigma_{i+1}\sigma_i\sigma_{i+1}\\)
    

 

presentation of braid groups

\(B_n\)

generators \(\sigma_1,...,\sigma_{n-1}\)

relations (known as the braid or Artin relations)\[\sigma_i\sigma_j =\sigma_j \sigma_i\] whenever \(|i-j| \geq 2 \)

\(\sigma_i\sigma_{i+1}\sigma_i = \sigma_{i+1}\sigma_i \sigma_{i+1}\) for \(i = 1,..., n-2\)Yang-Baxter equation (YBE)

 

 

related items

• Jones polynomials
  
• Hecke algebra
  

 

 

encyclopedia

• http://en.wikipedia.org/wiki/Braid_group
• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/
• http://www.proofwiki.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=

4909919

 

 

articles

 

• http://www.ams.org/mathscinet
• [1]http://www.zentralblatt-math.org/zmath/en/
• http://arxiv.org/
• http://www.pdf-search.org/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://dx.doi.org/

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/