Centralizer construction of the Yangian of the queer Lie superalgebra

被引:0
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作者
Nazarov, M [1 ]
Sergeev, A
机构
[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England
[2] Steklov Inst Math, St Petersburg 191011, Russia
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中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Consider the complex matrix Lie superalgebra g(l)N vertical bar N with the standard generators C E-ij where i, j = +/- l,..., +/- N. Define an involutive automorphism eta of g(l)N vertical bar N by eta(E-ij)= E-i,-j. The queer Lie superalgebra q(N) is the fixed point subalgebra in g(l)N vertical bar N relative to eta. Consider the twisted polynomial Current Lie superalgebra g={X(t)is an element of g(l)N vertical bar N[t]:eta(X(t))=X(-t)}. The enveloping algebra U(p) of the Lie superalgebra g has a deformation, called the Yangian of qN. For each M = 1, 2, denote by A(N)(M) the centralizer of q(M) subset of q N+M in the associative superalgebra U(qN+M).In this article we construct a sequence Of Surjective homornorphisms U(qN) <- A(N)(1)<- A(N)(2)....We describe the inverse limit of the sequence of centralizer algebras A(N)(1),A(N)(2),.... in terms of the Yangian Of qN.
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页码:417 / +
页数:3
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