On the classification of modular fusion algebras
On the classification of modular fusion algebras
复制标题
模融合代数的分类
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
W. Eholzer
中科院分区：
文献类型：
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作者：
W. Eholzer
引入了（非退化）强模融合代数的概念。这里强模意味着融合代数是由模群Γ=SL（2，n）的表示通过Verlinde公式导出的，其核包含一个同余子群。此外，非退化意味着可能的基础有理共形场论的共形维数不会相差整数。我们的主要结果是分类的所有强模融合代数的第二，第三和第四和分类的所有非退化强模融合代数的维数小于24。我们利用有限群的不可约表示的分类
$$SL（2，\mathbb {Z}_{p^\lambda }）$$
其中p是素数，λ是正整数。最后，我们给出了维数小于24的简单非退化强模融合代数的多项式实现和融合图。
AbstractWe introduce the notion of (nondegenerate) strongly-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the modular group Γ=SL(2,ℤ) whose kernel contains a congruence subgroup. Furthermore, nondegenerate means that the conformal dimensions of possibly underlying rational conformal field theories do not differ by integers. Our main result is the classification of all strongly-modular fusion algebras of dimension two, three and four and the classification of all nondegenerate strongly-modular fusion algebras of dimension less than 24. We use the classification of the irreducible representations of the finite groups
$$SL(2,\mathbb{Z}_{p^\lambda } )$$
, wherep is a prime and λ a positive integer. Finally, we give polynomial realizations and fusion graphs for all simple nondegenerate strongly-modular fusion algebras of dimension less than 24.