Affine cellularity of affine Yokonuma–Hecke algebras
Affine cellularity of affine Yokonuma–Hecke algebras
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仿射横沼赫克代数的仿射元胞性
DOI：
10.1016/j.jalgebra.2017.10.014
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发表时间：
2018
影响因子：
0.9
通讯作者：
Weideng Cui
中科院分区：
文献类型：
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作者：
Weideng Cui
我们建立了仿射Yokonuma-Hecke代数Y r，n(q)与a型仿射Hecke代数张量积中的系数矩阵代数的直接和之间的显式代数同构。应用这一结果，我们证明了Y r，n(q)在Koenig和Xi意义上是仿射元胞的，并进一步证明了当参数q不是poincar<s:1>多项式的根时，它具有有限的整体维数。作为另一个应用，我们还恢复了先前在[7]中得到的Y r，n(q)的模表示理论。
We establish an explicit algebra isomorphism between the affine Yokonuma–Hecke algebra Y r,n(q) and a direct sum of matrix algebras with coefficients in tensor products of affine Hecke algebras of type A. As an application of this result, we show that Y r,n(q) is affine cellular in the sense of Koenig and Xi, and further prove that it has finite global dimension when the parameter q is not a root of the Poincaré polynomial. As another application, we also recover the modular representation theory of Y r,n(q) previously obtained in [7].