Braid group - 편집 역사

2021년 2월 17일 (수) 09:36에 Pythagoras0님의 편집

2021-02-17T09:36:05Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T02:48:32Z

메타데이터: 새 문단

2020년 11월 16일 (월) 12:30에 Pythagoras0님의 편집

2020-11-16T12:30:51Z

2020년 11월 13일 (금) 15:21에 imported>Pythagoras0님의 편집

2020-11-13T15:21:01Z

imported>Pythagoras0: /* examples */

2017-05-24T02:33:30Z

examples

imported>Pythagoras0: /* presentation of braid groups */

2017-05-24T02:27:16Z

presentation of braid groups

imported>Pythagoras0: /* presentation of braid groups */

2017-05-24T02:07:53Z

presentation of braid groups

imported>Pythagoras0: /* related items */

2016-05-10T02:33:01Z

2014년 4월 4일 (금) 02:28에 imported>Pythagoras0님의 편집

2014-04-04T02:28:18Z

2013년 5월 9일 (목) 17:08에 imported>Pythagoras0님의 편집

2013-05-09T17:08:49Z

@@ 70번째 줄: / 70번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q220409 Q220409]

← 이전 판		2020년 12월 28일 (월) 02:48 판
69번째 줄:		69번째 줄:
	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q220409 Q220409]

@@ 26번째 줄: / 26번째 줄: @@
 ** <math>\sigma_i\sigma_{i+1}\sigma_i = \sigma_{i+1}\sigma_i \sigma_{i+1}</math> for <math>i = 1,..., n-2</math>
 * [[Yang-Baxter equation (YBE)]]
-* For a solution of the YBE $\bar{R}$, we can construct a representation $\rho$ of the braid group by
+* For a solution of the YBE <math>\bar{R}</math>, we can construct a representation <math>\rho</math> of the braid group by
-$$
+:<math>
 \rho : B_n \to \rm{Aut}(V^{\otimes n})
-$$ where $\rho(\sigma_i)=\bar{R}_i$
+</math> where <math>\rho(\sigma_i)=\bar{R}_i</math>
-There is also a natural surjective morphism from $B_n$ to the symmetric group $\mathfrak{S}_n$, given  on the generators by $B_n\ni\sigma_i\mapsto s_i\in \mathfrak{S}_n$, $i=1,\dots,n-1$. For a braid $\beta\in B_n$, we denote $p_{\beta}$ its image in $\mathfrak{S}_n$, and refer to $p_{\beta}$ as to the underlying permutation of $\beta$.
+There is also a natural surjective morphism from <math>B_n</math> to the symmetric group <math>\mathfrak{S}_n</math>, given  on the generators by <math>B_n\ni\sigma_i\mapsto s_i\in \mathfrak{S}_n</math>, <math>i=1,\dots,n-1</math>. For a braid <math>\beta\in B_n</math>, we denote <math>p_{\beta}</math> its image in <math>\mathfrak{S}_n</math>, and refer to <math>p_{\beta}</math> as to the underlying permutation of <math>\beta</math>.
@@ 39번째 줄: / 39번째 줄: @@
 [[파일:Braid.png]]
 * read the braid word from left to right accordingly.
-* For instance, the braid word corresponding to the braid above is $\sigma_1^{-1}\sigma_2\sigma_1^{-1}\sigma_2\sigma_1^{-1}$
+* For instance, the braid word corresponding to the braid above is <math>\sigma_1^{-1}\sigma_2\sigma_1^{-1}\sigma_2\sigma_1^{-1}</math>
 ==Markov moves==

← 이전 판		2020년 11월 13일 (금) 15:21 판
68번째 줄:		68번째 줄:
	[[분류:개인노트]]		[[분류:개인노트]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:migrate]]

@@ 36번째 줄: / 36번째 줄: @@
 ==examples==
-* in a braid diagram, read from bottom to top and we number all strands of the braid with the indices it starts at the bottom.
+* in a braid diagram, read from bottom to top and we number all strands of the braid with the indices it starts at the bottom
 * read the braid word from left to right accordingly.
-* For instance, the braid word corresponding to the braid on the left of Figure ? is $\sigma_1^{-1}\sigma_2\sigma_1^{-1}\sigma_2\sigma_1^{-1}$
+* For instance, the braid word corresponding to the braid above is $\sigma_1^{-1}\sigma_2\sigma_1^{-1}\sigma_2\sigma_1^{-1}$
 ==Markov moves==

← 이전 판		2017년 5월 24일 (수) 02:27 판
33번째 줄:		33번째 줄:

	There is also a natural surjective morphism from $B_n$ to the symmetric group $\mathfrak{S}_n$, given on the generators by $B_n\ni\sigma_i\mapsto s_i\in \mathfrak{S}_n$, $i=1,\dots,n-1$. For a braid $\beta\in B_n$, we denote $p_{\beta}$ its image in $\mathfrak{S}_n$, and refer to $p_{\beta}$ as to the underlying permutation of $\beta$.		There is also a natural surjective morphism from $B_n$ to the symmetric group $\mathfrak{S}_n$, given on the generators by $B_n\ni\sigma_i\mapsto s_i\in \mathfrak{S}_n$, $i=1,\dots,n-1$. For a braid $\beta\in B_n$, we denote $p_{\beta}$ its image in $\mathfrak{S}_n$, and refer to $p_{\beta}$ as to the underlying permutation of $\beta$.
		+
		+
		+	==examples==
		+	* in a braid diagram, read from bottom to top and we number all strands of the braid with the indices it starts at the bottom.
		+	* read the braid word from left to right accordingly.
		+	* For instance, the braid word corresponding to the braid on the left of Figure ? is $\sigma_1^{-1}\sigma_2\sigma_1^{-1}\sigma_2\sigma_1^{-1}$

	==Markov moves==		==Markov moves==

← 이전 판		2017년 5월 24일 (수) 02:07 판
31번째 줄:		31번째 줄:
	$$ where $\rho(\sigma_i)=\bar{R}_i$		$$ where $\rho(\sigma_i)=\bar{R}_i$

		+
		+	There is also a natural surjective morphism from $B_n$ to the symmetric group $\mathfrak{S}_n$, given on the generators by $B_n\ni\sigma_i\mapsto s_i\in \mathfrak{S}_n$, $i=1,\dots,n-1$. For a braid $\beta\in B_n$, we denote $p_{\beta}$ its image in $\mathfrak{S}_n$, and refer to $p_{\beta}$ as to the underlying permutation of $\beta$.

	==Markov moves==		==Markov moves==

@@ 46번째 줄: / 46번째 줄: @@
 * [[Jones polynomials]]
 * [[Hecke algebra]]
+* [[Loop braid group]]
 ==encyclopedia==