Cell structures for the Yokonuma–Hecke algebra and the algebra of braids and ties
Cell structures for the Yokonuma–Hecke algebra and the algebra of braids and ties
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DOI：
10.1016/j.jpaa.2018.02.001
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发表时间：
2015-06
影响因子：
0.8
通讯作者：
J. Espinoza;S. Ryom-Hansen
中科院分区：
文献类型：
--
作者：
J. Espinoza;S. Ryom-Hansen
我们构造了Yokonuma-Hecke代数Y r， n的忠实张量表示，并利用它给出了Y r， n与Shoji的修正Ariki-Koike代数之间的具体同构。我们给出Y r， n的元胞基，并证明Y r， n的jusys - murphy元是抽象意义上的jm元。最后，我们构造了辫子和领带的aicardii - juyumaya代数的元胞基。
We construct a faithful tensor representation for the Yokonuma–Hecke algebra Y r, n, and use it to give a concrete isomorphism between Y r, n and Shoji's modified Ariki–Koike algebra. We give a cellular basis for Y r, n and show that the Jucys–Murphy elements for Y r, n are JM-elements in the abstract sense. Finally, we construct a cellular basis for the Aicardi–Juyumaya algebra of braids and ties.