Yangian of the queer Lie superalgebra

被引:33
|
作者
Nazarov, M [1 ]
机构
[1] Univ York, Dept Math, York YO1 5DD, N Yorkshire, England
关键词
D O I
10.1007/s002200050754
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Consider the complex matrix Lie superalgebra g(N/N)(I) With the standard generators E-ij, where i, j = +/-1, ... ,+/-N. Define an involutory automorphism eta of g(N/N)(I) by eta(E-ij) = E-i,(-j). The twisted polynomial current Lie superalgebra g = {X(u) is an element of g(N/N)(I) [u] : eta(X(u)) = X(-u)} has a natural Lie co-superalgebra structure. We quantise the universal enveloping algebra U(g) as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld. We also construct a wide class of irreducible representations of the quantised algebra.
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页码:195 / 223
页数:29
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