| Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra |
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| 引用本文： | DUPLIJ Steven KOTULSKA Olga SADOVNIKOV Alexander. Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra[J]. 浙江大学学报(A卷英文版), 2005, 6(10): 1065-1079 |
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| 作者姓名： | DUPLIJ Steven KOTULSKA Olga SADOVNIKOV Alexander |
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| 作者单位： | Department of Physics and Technology，V.N. Karazin Kharkov National University，Svoboda Sq. 4，Kharkov 61077，Ukraine，Department of Physics and Technology，V.N. Karazin Kharkov National University，Svoboda Sq. 4，Kharkov 61077，Ukraine，Department of Physics and Technology，V.N. Karazin Kharkov National University，Svoboda Sq. 4，Kharkov 61077，Ukraine |
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| 摘 要： | INTRODUCTION The Yang-Baxter equation(Yang,1967;Baxter,1972)is one of the most valuable concepts in modern theoretical physics(Baxter,1982).The importance of detailed study of Yang-Baxter equation solutions is due to its key role in constant solution models of sta-tistics mechanics(Baxter,1972;1982)and field the-ory in lower dimensions(Yang,1967),conformal field theory(Di Francesco et al.,1997)and in quan-tum integrable systems(Faddeev et al.,1990).From the group-theoretical viewpoint…
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| 关 键 词： | 量子论 Yang-Baxter方程 R矩阵 规则性 |
| 收稿时间： | 2005-03-10 |
| 修稿时间： | 2005-06-25 |
Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra |
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| DUPLIJ Steven,KOTULSKA Olga,SADOVNIKOV Alexander. Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra[J]. Journal of Zhejiang University Science, 2005, 6(10): 1065-1079 |
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| Authors: | DUPLIJ Steven KOTULSKA Olga SADOVNIKOV Alexander |
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| Abstract: | Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix.The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied.As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered. |
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| Keywords: | Constant solution Grassmann algebra Regularity R-matrix |
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