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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.10 P.1065-1079


Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra

Author(s):  DUPLIJ Steven, KOTULSKA Olga, SADOVNIKOV Alexander

Affiliation(s):  Department of Physics and Technology, V.N. Karazin Kharkov National University, Svoboda Sq. 4, Kharkov 61077, Ukraine

Corresponding email(s):   Steven.A.Duplij@univer.kharkov.ua

Key Words:  Constant solution, Grassmann algebra, Regularity, R-matrix

DUPLIJ Steven, KOTULSKA Olga, SADOVNIKOV Alexander. Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra[J]. Journal of Zhejiang University Science A, 2005, 6(10): 1065-1079.

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author="DUPLIJ Steven, KOTULSKA Olga, SADOVNIKOV Alexander",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

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%A DUPLIJ Steven
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%I Zhejiang University Press & Springer
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T1 - Quantum Yang-Baxter equation and constant R-matrix over Grassmann algebra
A1 - DUPLIJ Steven
A1 - SADOVNIKOV Alexander
J0 - Journal of Zhejiang University Science A
VL - 6
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SP - 1065
EP - 1079
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2005.A1065

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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