R-matrix - 편집 역사

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

2021-02-17T09:17:27Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-27T11:56:38Z

메타데이터: 새 문단

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-27T11:51:13Z

메타데이터: 새 문단

2020년 11월 16일 (월) 12:33에 Pythagoras0님의 편집

2020-11-16T12:33:46Z

2020년 11월 16일 (월) 10:36에 Pythagoras0님의 편집

2020-11-16T10:36:45Z

2020년 11월 14일 (토) 01:39에 imported>Pythagoras0님의 편집

2020-11-14T01:39:25Z

imported>Pythagoras0: /* related items */

2016-05-06T01:21:44Z

imported>Pythagoras0: /* articles */

2014-09-23T08:13:12Z

articles

imported>Pythagoras0: /* permuted R-matrix */

2014-03-19T11:40:10Z

permuted R-matrix

2014년 2월 26일 (수) 17:24에 imported>Pythagoras0님의 편집

2014-02-26T17:24:00Z

@@ 119번째 줄: / 119번째 줄: @@
 * ID :  [https://www.wikidata.org/wiki/Q2993305 Q2993305]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
-* ID :  [https://www.wikidata.org/wiki/Q7273285 Q7273285]
+* ID :  [https://www.wikidata.org/wiki/Q2993305 Q2993305]

← 이전 판		2020년 12월 27일 (일) 11:56 판
118번째 줄:		118번째 줄:
	===위키데이터===		===위키데이터===
	* ID : [https://www.wikidata.org/wiki/Q2993305 Q2993305]		* ID : [https://www.wikidata.org/wiki/Q2993305 Q2993305]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q7273285 Q7273285]

← 이전 판		2020년 12월 27일 (일) 11:51 판
113번째 줄:		113번째 줄:
	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q2993305 Q2993305]

@@ 10번째 줄: / 10번째 줄: @@
 ==YBE==
 * R-matrix is a solution of the [[Yang-Baxter equation (YBE)]]
-$$R_{12}(u)R_{13}(u+v)R_{23}(v)=R_{23}(v)R_{13}(u+v)R_{12}(u)$$
+:<math>R_{12}(u)R_{13}(u+v)R_{23}(v)=R_{23}(v)R_{13}(u+v)R_{12}(u)</math>
-* $R(u,\eta)$
+* <math>R(u,\eta)</math>
-** $u$ is called the spectral parameter
+** <math>u</math> is called the spectral parameter
-** $\eta$ quantum paramter (or semi-classical parameter)
+** <math>\eta</math> quantum paramter (or semi-classical parameter)
-* ignoring $\eta$, we get the classical R-matrix $R(u)$ in $U(\mathfrak{g})$
+* ignoring <math>\eta</math>, we get the classical R-matrix <math>R(u)</math> in <math>U(\mathfrak{g})</math>
-* ignoring $u$, we get $R(\eta)$ in $U_{q}(\mathfrak{g})$ where $q=e^{\eta}$
+* ignoring <math>u</math>, we get <math>R(\eta)</math> in <math>U_{q}(\mathfrak{g})</math> where <math>q=e^{\eta}</math>
 ** found by Drinfeld and Jimbo
 ** see [[Drinfeld-Jimbo quantum groups (quantized UEA)]]
@@ 31번째 줄: / 31번째 줄: @@
 ===derivation of \ref{braid} from the YBE===
-* $\bar R_{2}(u)\bar R_1(u+v) \bar R_{2}(v)$ corresponding to $R_{12}(u)R_{13}(u+v)R_{23}(v)$ can be written as
+* <math>\bar R_{2}(u)\bar R_1(u+v) \bar R_{2}(v)</math> corresponding to <math>R_{12}(u)R_{13}(u+v)R_{23}(v)</math> can be written as
-$$
+:<math>
 (1,2,3) \xrightarrow{R_{23}} (1,2',3') \xrightarrow{P_{23}} (1,3',2') \xrightarrow{R_{12}} (1',3'',2') \xrightarrow{P_{12}} (3'',1',2')\xrightarrow{R_{23}} (3'',1'',2'')\xrightarrow{P_{23}} (3'',2'',1'')
-$$
+</math>
-* $\bar R_{1}(v)\bar R_2(u+v) \bar R_{1}(u)$ corresponding to $R_{23}(v)R_{13}(u+v)R_{12}(u)$ can be written as
+* <math>\bar R_{1}(v)\bar R_2(u+v) \bar R_{1}(u)</math> corresponding to <math>R_{23}(v)R_{13}(u+v)R_{12}(u)</math> can be written as
-$$
+:<math>
 (1,2,3) \xrightarrow{R_{12}} (1',2',3) \xrightarrow{P_{12}} (2',1',3) \xrightarrow{R_{23}} (2,1'',3') \xrightarrow{P_{23}} (2,3',1'')\xrightarrow{R_{12}} (2'',3'',1'')\xrightarrow{P_{12}} (3'',2'',1'')
-$$
+</math>
 ==R-matrix and Braid groups==
@@ 46번째 줄: / 46번째 줄: @@
 ==examples of R-matrix==
 * rational R-matrix
-$$
+:<math>
 \left(
 \begin{array}{cccc}
@@ 55번째 줄: / 55번째 줄: @@
 \end{array}
 \right)
-$$
+</math>
 * trigonometric R-matrix
-$$
+:<math>
 \left(
 \begin{array}{cccc}
@@ 66번째 줄: / 66번째 줄: @@
 \end{array}
 \right)
-$$
+</math>
@@ 104번째 줄: / 104번째 줄: @@
 ==articles==
-* Lentner, Simon, and Daniel Nett. “New $R$-Matrices for Small Quantum Groups.” arXiv:1409.5824 [math], September 19, 2014. http://arxiv.org/abs/1409.5824.
+* Lentner, Simon, and Daniel Nett. “New <math>R</math>-Matrices for Small Quantum Groups.” arXiv:1409.5824 [math], September 19, 2014. http://arxiv.org/abs/1409.5824.
 *  R-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators

@@ 105번째 줄: / 105번째 줄: @@
 ==articles==
 * Lentner, Simon, and Daniel Nett. “New $R$-Matrices for Small Quantum Groups.” arXiv:1409.5824 [math], September 19, 2014. http://arxiv.org/abs/1409.5824.
-*  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

← 이전 판		2020년 11월 14일 (토) 01:39 판
112번째 줄:		112번째 줄:
	[[분류:quantum groups]]		[[분류:quantum groups]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:migrate]]

@@ 90번째 줄: / 90번째 줄: @@
 ==related items==
 * [[Yang-Baxter equation (YBE)]]
+* [[R-matrix in quantum affine algebra]]
 ==computational resource==

@@ 23번째 줄: / 23번째 줄: @@
 * For <math>R</math> matrix on <math>V \otimes V</math>, define the permuted R-matrix <math>\bar R=p\circ R</math> where <math>p</math> is the permutation map.
 * define <math>\bar R_i</math> sitting in i and i+1 th slot by
-:<math>\bar R_i=1\otimes \cdots \otimes\bar R \cdots \otimes 1</math>
+:<math>\bar R_i=1\otimes \cdots \otimes\bar R\otimes \cdots \otimes 1</math>
 * whenever <math>|i-j| \geq 2 </math>, we have <math>\bar R_i\bar R_j =\bar R_j\bar R_i</math>
 * the YBE reduces to