Monoidal categorifications of cluster algebras - 편집 역사

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@@ 11번째 줄: / 11번째 줄: @@
 ==monoidal categorification==
-* $A$ : cluster algebra
+* <math>A</math> : cluster algebra
-* $M$ : monoidal categorify
+* <math>M</math> : monoidal categorify
-* $M$ is a monoidal categorification of $A$ if the Grothendieck ring $K_0(M)$ of $M$ is isomorphic to $A$ which induces bijection between
+* <math>M</math> is a monoidal categorification of <math>A</math> if the Grothendieck ring <math>K_0(M)</math> of <math>M</math> is isomorphic to <math>A</math> which induces bijection between
-# cluster monomials of $A$
+# cluster monomials of <math>A</math>
-# the classes of real simple objects of $M$ where $V$ is ''real'' if $V\otimes V$ is simple
+# the classes of real simple objects of <math>M</math> where <math>V</math> is ''real'' if <math>V\otimes V</math> is simple
-* cluster variables of $A$ (including coefficients) corresponds to classes of real prime simple objects
+* cluster variables of <math>A</math> (including coefficients) corresponds to classes of real prime simple objects
 ===proposition===
-* Suppose that $A$ has a monoidal categorification $M$ and also that each object $B$ in $M$ has unique finite composition series, (i.e., find simple subobject $A_1$, then simple subobject of $A_2$ of $B/A_1$, etc ... composition series if colleciton of all $A$'s)
+* Suppose that <math>A</math> has a monoidal categorification <math>M</math> and also that each object <math>B</math> in <math>M</math> has unique finite composition series, (i.e., find simple subobject <math>A_1</math>, then simple subobject of <math>A_2</math> of <math>B/A_1</math>, etc ... composition series if colleciton of all <math>A</math>'s)
 * Then
 # each cluster variable of a has positivie Laurent expansion with respect to any cluster
@@ 60번째 줄: / 60번째 줄: @@
 * Kang, Seok-Jin, Masaki Kashiwara, Myungho Kim, and Se-jin Oh. ‘Monoidal Categorification of Cluster Algebras II’. arXiv:1502.06714 [math], 24 February 2015. http://arxiv.org/abs/1502.06714.
 * Kang, Seok-Jin, Masaki Kashiwara, Myungho Kim, and Se-jin Oh. “Monoidal Categorification of Cluster Algebras.” arXiv:1412.8106 [math], December 27, 2014. http://arxiv.org/abs/1412.8106.
-* Ma, Hai-Tao, Yan-Min Yang, and Zhu-Jun Zheng. “Quantum Cluster Algebra Structure on the Finite Dimensional Representations of $U_q(\widehat{sl_{2}})$.” arXiv:1406.2452 [math-Ph], June 10, 2014. http://arxiv.org/abs/1406.2452.
+* Ma, Hai-Tao, Yan-Min Yang, and Zhu-Jun Zheng. “Quantum Cluster Algebra Structure on the Finite Dimensional Representations of <math>U_q(\widehat{sl_{2}})</math>.” arXiv:1406.2452 [math-Ph], June 10, 2014. http://arxiv.org/abs/1406.2452.
-* Yang, Yan-Min, and Zhu-Jun Zheng. 2014. “Cluster Algebra Structure on the Finite Dimensional Representations of $U_q(\widehat{A_{3}})$ for $l$=2.” arXiv:1403.5124 [math-Ph], March. http://arxiv.org/abs/1403.5124.
+* Yang, Yan-Min, and Zhu-Jun Zheng. 2014. “Cluster Algebra Structure on the Finite Dimensional Representations of <math>U_q(\widehat{A_{3}})</math> for <math>l</math>=2.” arXiv:1403.5124 [math-Ph], March. http://arxiv.org/abs/1403.5124.
 * Hernandez, David, and Bernard Leclerc. ‘Monoidal Categorifications of Cluster Algebras of Type A and D’. arXiv:1207.3401 [math], 14 July 2012. http://arxiv.org/abs/1207.3401.
 * Nakajima, Hiraku. 2011. “Quiver varieties and cluster algebras”. <em>Kyoto Journal of Mathematics</em> 51 (1): 71-126. doi:10.1215/0023608X-2010-021.

← 이전 판		2020년 11월 13일 (금) 14:06 판
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	[[분류:math]]		[[분류:math]]
	[[분류:quantum groups]]		[[분류:quantum groups]]
		+	[[분류:migrate]]

← 이전 판		2015년 6월 15일 (월) 01:11 판
70번째 줄:		70번째 줄:
	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:math]]		[[분류:math]]
		+	[[분류:quantum groups]]

@@ 62번째 줄: / 62번째 줄: @@
 * Ma, Hai-Tao, Yan-Min Yang, and Zhu-Jun Zheng. “Quantum Cluster Algebra Structure on the Finite Dimensional Representations of $U_q(\widehat{sl_{2}})$.” arXiv:1406.2452 [math-Ph], June 10, 2014. http://arxiv.org/abs/1406.2452.
 * Yang, Yan-Min, and Zhu-Jun Zheng. 2014. “Cluster Algebra Structure on the Finite Dimensional Representations of $U_q(\widehat{A_{3}})$ for $l$=2.” arXiv:1403.5124 [math-Ph], March. http://arxiv.org/abs/1403.5124.
-* David Hernandez, Bernard Leclerc , Monoidal categorifications of cluster algebras of type A and D http://arxiv.org/abs/1207.3401
+* Hernandez, David, and Bernard Leclerc. ‘Monoidal Categorifications of Cluster Algebras of Type A and D’. arXiv:1207.3401 [math], 14 July 2012. http://arxiv.org/abs/1207.3401.
 * Nakajima, Hiraku. 2011. “Quiver varieties and cluster algebras”. <em>Kyoto Journal of Mathematics</em> 51 (1): 71-126. doi:10.1215/0023608X-2010-021.

@@ 58번째 줄: / 58번째 줄: @@
 ==articles==
 * Kang, Seok-Jin, Masaki Kashiwara, Myungho Kim, and Se-jin Oh. “Monoidal Categorification of Cluster Algebras.” arXiv:1412.8106 [math], December 27, 2014. http://arxiv.org/abs/1412.8106.
 * Ma, Hai-Tao, Yan-Min Yang, and Zhu-Jun Zheng. “Quantum Cluster Algebra Structure on the Finite Dimensional Representations of $U_q(\widehat{sl_{2}})$.” arXiv:1406.2452 [math-Ph], June 10, 2014. http://arxiv.org/abs/1406.2452.

@@ 40번째 줄: / 40번째 줄: @@
 * [[Additive categorifications of cluster algebras]]
 * [[categorification of quantum groups]]
 * [[Coordinate ring of maximal unipotent subgroup]]