Braid group

review of symmetric groups

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

 

 

presentation

• 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}\\)
    

 

introduction

\(B_n\)

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)

 

 

 

 

books

• 찾아볼 수학책
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Braid_group
• http://en.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(첨부파일로 올릴것)

 

blogs

• 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
• 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=

 

articles

• 논문정리
• http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html

• 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=