"Braid group"의 두 판 사이의 차이

2009년 9월 20일 (일) 20:39 판

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 \(i = 1,..., n-2\) (sometimes called the Yang-Baxter equation)

related items

books

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=

@@ 1번째 줄: / 1번째 줄: @@
+<h5>review of symmetric groups</h5>
+* 원소의 개수가 n인 집합의 전단사함수들의 모임
+* <math>n!</math> 개의 원소가 존재함
+* 대칭군의 부분군은 치환군(permutation group)이라 불림
+<h5 style="margin: 0px; line-height: 2em;">presentation</h5>
+*  생성원 <math>\sigma_1, \ldots, \sigma_{n-1}</math><br>
+*  relations<br>
+** <math>{\sigma_i}^2 = 1</math><br>
+** <math>\sigma_i\sigma_j = \sigma_j\sigma_i \mbox{ if } j \neq i\pm 1</math><br>
+** <math>\sigma_i\sigma_{i+1}\sigma_i = \sigma_{i+1}\sigma_i\sigma_{i+1}\</math><br>
+<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">introduction</h5>
+<math>B_n</math>
+generators <math>\sigma_1,...,\sigma_{n-1}</math>
+relations (known as the braid or Artin relations):
+<math>\sigma_i\sigma_j =\sigma_j \sigma_i</math> whenever <math>|i-j| \geq 2 </math>
+<math>\sigma_i\sigma_{i+1}\sigma_i = \sigma_{i+1}\sigma_i \sigma_{i+1}</math> for <math>i = 1,..., n-2</math> (sometimes called the Yang-Baxter equation)
+<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">related items</h5>
+<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books</h5>
+* [[2009년 books and articles|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=
+<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
+* 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)
+<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">blogs</h5>
+* 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
+* 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=
+<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5>
+* [[2010년 books and 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/%7Ereb/papers/index.html 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=
+<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">TeX </h5>