Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (5): 1267-1294.doi: 10.1016/S0252-9602(09)60103-X

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SOLVING COLORED YANG-BAXTER EQUATION BY WU'S METHOD

 REN Xin-An, WANG Shi-Kun, WU Ke   

  1. 1.Department of Mathematics, China University of Mining and Technology, |Xuzhou 221116, China
    2.Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China
    3.KLMM, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China
    4.Department of Mathematics, Capital Normal University, Beijing 100048, China
  • Received:2007-03-30 Revised:2007-09-24 Online:2009-09-20 Published:2009-09-20
  • Supported by:

    The project partially supported by NKBRPC (2004CB31800, 2006CB805905) and Knowledge Innovation Funds of  CAS (KJCX3-SYW-S03)

Abstract:

In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu's method. It is also proved that the solutions are composed of six groups of basic solutions up to five solution transformations. Moreover, all solutions can be classified into two categories called Baxter type and free-fermion type.

Key words: Yang Baxter equation, solution of the colored Yang Baxter equatio, Wus method

CLC Number: 

  • 17B65
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