结合超代数上的超结合Yang-Baxter方程
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摘要
主要研究结合超代数上的超结合Yang-Baxter方程.首先给出结合超代数上Rota-Baxter算子和■-算子的定义,得到结合超代数上奇的Rota-Baxter算子与李超代数上奇的Rota-Baxter算子之间的关系,找到结合超代数上的超结合Yang-Baxter方程的解与结合超代数上的■-算子之间的关系.最后给出了结合超代数上超结合YangBaxter方程的解与超2-上循环之间的关系.
In this paper we study the super associative Yang-Baxter equation in associative superalgebras.First we give the definition of Rota-Baxter operator and ■-operator in associative superalgebra.We also give the relation between the odd Rota-Baxter operator in associative superalgebra and Lie superalgebra.Then we give the relation between the solution of super associative Yang-Baxter equation and ■-operator in associative superalgebra.At last,we give the relation between the solution of super associative Yang-Baxter equation and super 2-cocycle in associative superalgebra.
In this paper we study the super associative Yang-Baxter equation in associative superalgebras.First we give the definition of Rota-Baxter operator and ■-operator in associative superalgebra.We also give the relation between the odd Rota-Baxter operator in associative superalgebra and Lie superalgebra.Then we give the relation between the solution of super associative Yang-Baxter equation and ■-operator in associative superalgebra.At last,we give the relation between the solution of super associative Yang-Baxter equation and super 2-cocycle in associative superalgebra.
引文
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[7]WANG Y,HOU D,BAI C.Operator forms of the classical Yang-Baxter equation in Lie superalgebras[J].Int J Geom Meth Modern Phys,2010,7(4):583-597.
[8]ABDAOUI K,MABROUK S,MAKHLOUF A.Rota-Baxter operators on pre-Lie superalgebras and beyond[J].arXiv:1512.08043.
[2]FADDEEV L D,TAKHTAJAN L.The quantum inverse scattering method of the inverse problem and the Heisenberg XYZ model[J].Russ Math Surv,1979,34:11-68.
[3]CHARI V,PRESSLEY A.A guide to quantum groups[M].Cambridge:Cambridge University Press,1994.
[4]BAXTER G.An analytic problem whose solution follows from a simple algebraic identity[J].Pacific J Math,1960,10(3):731-742.
[5]ROTA G C.Baxter operators,an introduction[C]∥KUNG J P S.Gian-Carlo Rota on combinatorics:Introductory papers and commentaries.Boston:Birkhauser,1995.
[6]BORDEMANN M.Generalized Lax pairs,the modified classical Yang-Baxter equation,and affine geometry of Lie groups[J].Comm Math Phys,1990,135(1):201-216.
[7]WANG Y,HOU D,BAI C.Operator forms of the classical Yang-Baxter equation in Lie superalgebras[J].Int J Geom Meth Modern Phys,2010,7(4):583-597.
[8]ABDAOUI K,MABROUK S,MAKHLOUF A.Rota-Baxter operators on pre-Lie superalgebras and beyond[J].arXiv:1512.08043.