On realization of fusion rings from generalized Cartan matrices
On realization of fusion rings from generalized Cartan matrices
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DOI：
10.1007/s10114-016-6088-9
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
Zhi Hua Wang;Li Bin Li-Li-Bin-Li-2193117382
中科院分区：
文献类型：
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作者：
Zhi Hua Wang;Li Bin Li-Li-Bin-Li-2193117382
熔合环（R，B）的卡西米尔元素产生了所谓的卡西米尔矩阵（R，B）。这使我们能够在Kac意义上构造一个适合对角矩阵d的广义Cartan矩阵d−。本文研究了卡西米尔矩阵的一些初等性质，并利用这些性质从广义卡坦矩阵（d−c）得到了某些融合环。仿射)类型。结果表明，存在一个d−c为有限熵的熔合环。仿射)类型if and only if d−Chas only formA2（respo . a1(1)）。我们还实现了d−c是一个特定的不定型广义Cartan矩阵的所有融合环。
The Casimir element of a fusion ring (R,B) gives rise to the so called Casimir matrixCof (R,B). This enables us to construct a generalized Cartan matrixD−Cin the sense of Kac for a suitable diagonal matrixD. In this paper, we study some elementary properties of the Casimir matrixCand use them to realize certain fusion rings from the generalized Cartan matrixD−Cof finite (resp. affine) type. It turns out that there exists a fusion ring withD−Cbeing of finite (resp. affine) type if and only ifD−Chas only the formA2(resp.A1(1)). We also realize all fusion rings withD−Cbeing a particular generalized Cartan matrix of indefinite type.