"R-matrix"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| − | + | ==introduction== | |
* R-matrix has entries from Boltzman weights. | * R-matrix has entries from Boltzman weights. | ||
* From quantum group point of view, R-matrix naturally appears as intertwiners of tensor product of two evaluation modules | * From quantum group point of view, R-matrix naturally appears as intertwiners of tensor product of two evaluation modules | ||
| − | * | + | * from this intertwining property we need to consider <math>\bar R=p\circ R</math> instead of the <math>R</math> matrix where <math>p</math> is the permutation map |
| − | * this is | + | * this is what makes the module category into braided monoidal category |
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| − | + | ==YBE== | |
* [[Yang-Baxter equation (YBE)|Yang-Baxter equation]]<br><math>R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}</math><br> | * [[Yang-Baxter equation (YBE)|Yang-Baxter equation]]<br><math>R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}</math><br> | ||
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| − | + | ==R-matrix and Braid groups== | |
| − | * | + | * For <math>R</math> matrix on <math>V \otimes V</math>, define <math>\bar R=p\circ R</math> where <math>p</math> is the permutation map.<br><math>\bar R_i=1\otimes \cdots \otimes\bar R \cdots \otimes 1</math>, <math>\bar R_i</math> sitting in i and i+1 th slot.<br> |
| − | * Then YB reduces to<br><math>\bar R_i\bar R_j =\bar R_j\bar R_i</math> | + | * Then YB reduces to<br><math>\bar R_i\bar R_j =\bar R_j\bar R_i</math> whenever <math>|i-j| \geq 2 </math><br><math>\bar R_i\bar R_{i+1}\bar R_i= \bar R_{i+1}\bar R_i \bar R_{i+1}</math><br> which are the [[Braid group]] relations.<br> |
* with an R-matrix satisfying the YBE, we obtain a representation of the [[Braid group]], which then gives a link invariant in [[Knot theory]]<br> | * with an R-matrix satisfying the YBE, we obtain a representation of the [[Braid group]], which then gives a link invariant in [[Knot theory]]<br> | ||
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| − | + | ==related items== | |
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| − | + | ==books== | |
* [[2009년 books and articles|찾아볼 수학책]] | * [[2009년 books and articles|찾아볼 수학책]] | ||
| 47번째 줄: | 47번째 줄: | ||
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | * http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | ||
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| − | + | ==encyclopedia== | |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 60번째 줄: | 60번째 줄: | ||
* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]]) | * Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]]) | ||
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| − | + | ==blogs== | |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
| 71번째 줄: | 71번째 줄: | ||
** http://blogsearch.google.com/blogsearch?q= | ** http://blogsearch.google.com/blogsearch?q= | ||
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| − | + | ==articles== | |
* R-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators<br> | * R-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators<br> | ||
| 87번째 줄: | 87번째 줄: | ||
* http://dx.doi.org/ | * http://dx.doi.org/ | ||
| − | + | ||
| − | + | ==TeX == | |
2012년 10월 26일 (금) 11:20 판
introduction
- R-matrix has entries from Boltzman weights.
- From quantum group point of view, R-matrix naturally appears as intertwiners of tensor product of two evaluation modules
- from this intertwining property we need to consider \(\bar R=p\circ R\) instead of the \(R\) matrix where \(p\) is the permutation map
- this is what makes the module category into braided monoidal category
YBE
- Yang-Baxter equation
\(R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}\)
R-matrix and Braid groups
- For \(R\) matrix on \(V \otimes V\), define \(\bar R=p\circ R\) where \(p\) is the permutation map.
\(\bar R_i=1\otimes \cdots \otimes\bar R \cdots \otimes 1\), \(\bar R_i\) sitting in i and i+1 th slot. - Then YB reduces to
\(\bar R_i\bar R_j =\bar R_j\bar R_i\) whenever \(|i-j| \geq 2 \)
\(\bar R_i\bar R_{i+1}\bar R_i= \bar R_{i+1}\bar R_i \bar R_{i+1}\)
which are the Braid group relations. - with an R-matrix satisfying the YBE, we obtain a representation of the Braid group, which then gives a link invariant in Knot theory
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/Braided_monoidal_category
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
blogs
- 구글 블로그 검색
articles
- R-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators
- 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://www.ams.org/mathscinet
- 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=
- http://dx.doi.org/