$W^{(2)}_n$ algebras
$W^{(2)}_n$ algebras
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$W^{(2)}_n$代数
DOI：
10.1016/j.nuclphysb.2004.06.056
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
A. Semikhatov
中科院分区：
文献类型：
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作者：
B. Feigin;A. Semikhatov
我们构造了由两个流E和F生成的具有其OPE中n阶最高极点的sl-旋转式(2)代数-W代数W{subn}{sup(2)}的W-代数推广.这一系列中的n=3项是Bershadsky-Polyakov W{sub3}{sup(2)}代数。我们将这些代数定义为Uqs-bar(n个垂直bar 1)量子超群的中心化子(交换子)，并显式地找到了因式分解的‘Miura-like’形式的生成元。W{subn}{sup(2)}代数的另一种构造是关于陪集sl-旋转式(n竖杆1)/sl-旋转式(N)。这两个结构之间的关系涉及到两个sl-回旋(N)代数的k级和k‘级之间的’对偶‘(k+n-1)(k’+n-1)=1。
We construct W-algebra generalizations of the sl-circumflex(2) algebra-W algebras W{sub n}{sup (2)} generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky-Polyakov W{sub 3}{sup (2)} algebra. We define these algebras as a centralizer (commutant) of the Uqs-bar (n vertical bar 1) quantum supergroup and explicitly find the generators in a factored, 'Miura-like' form. Another construction of the W{sub n}{sup (2)} algebras is in terms of the coset sl-circumflex(n vertical bar 1)/sl-circumflex(n). The relation between the two constructions involves the 'duality' (k+n-1)(k'+n-1)=1 between levels k and k' of two sl-circumflex(n) algebras.