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Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue (10): 11-    DOI: 10.1631/jzus.2005.A1065
    
Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra
DUPLIJ Steven, KOTULSKA Olga, SADOVNIKOV Alexander
Department of Physics and Technology, V.N. Karazin Kharkov National University, Svoboda Sq. 4, Kharkov 61077, Ukraine
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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.

Key wordsConstant solution      Grassmann algebra      Regularity      R-matrix     
Received: 10 March 2005     
CLC:  O13  
Cite this article:

DUPLIJ Steven, KOTULSKA Olga, SADOVNIKOV Alexander. Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(10): 11-.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.A1065     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/I10/11

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