论文标题
在丝带类别的单元顶点代数上
On ribbon categories for singlet vertex algebras
论文作者
论文摘要
我们为每个Singlet顶点操作员代数$ \ MATHCAL {M}（P）$，$ P \ geq 2 $构造了两个非避免编织的色带张量类别。第一类包括所有有限长度$ \ Mathcal {M}（P）$ - 具有非典型组成因子的模块，而第二个模块是诱导Triplet Vertex Opertex操作员代数$ \ Mathcal $ \ Mathcal {W}（w}（p）$的模块的子类别。我们表明，每个不可约的模块都在这些类别的第二个类别中都有投影覆盖，尽管不是第一个，我们计算了所有涉及非典型不可减至模块及其投影覆盖物的融合产品。
We construct two non-semisimple braided ribbon tensor categories of modules for each singlet vertex operator algebra $\mathcal{M}(p)$, $p\geq 2$. The first category consists of all finite-length $\mathcal{M}(p)$-modules with atypical composition factors, while the second is the subcategory of modules that induce to local modules for the triplet vertex operator algebra $\mathcal{W}(p)$. We show that every irreducible module has a projective cover in the second of these categories, although not in the first, and we compute all fusion products involving atypical irreducible modules and their projective covers.
