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Stability of the centers of the symplectic group rings Z[Sp2n(q)]
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.jalgebra.2020.12.019 Şafak Özden
中文翻译:
辛群环中心的稳定性
更新日期:2021-01-08
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.jalgebra.2020.12.019 Şafak Özden
We investigate the structure constants of the center of the group algebra over a finite field. The reflection length on the group induces a filtration on the algebras . We prove that the structure constants of the associated graded algebra are independent of n. As tool in the proof we consider the embedding and determine the behavior of the centralizers and intersection of centralizers under the embedding . We determine explicit formulas for rate of the growth of the centralizer of an element in terms of dimension of the fixed space of U.
中文翻译:
辛群环中心的稳定性
我们研究中心的结构常数 群代数 在一个有限的领域。在组上的反射长度 诱导代数上的过滤 。我们证明了相关梯度代数的结构常数独立于n。作为证明的工具,我们考虑嵌入 并确定嵌入下扶正器和扶正器交点的行为 。我们确定元素扶正剂增长率的明确公式根据U的固定空间的尺寸。