Braid group
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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}\\)
- \({\sigma_i}^2 = 1\)
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)
encyclopedia
- http://en.wikipedia.org/wiki/Braid_group
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
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
- 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)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field