Structure of blocks with normal defect and abelian inertial quotient
Structure of blocks with normal defect and abelian inertial quotient
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具有正态缺陷和阿贝尔惯性商的块的结构
DOI：
10.1017/fms.2023.13
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Benson D
中科院分区：
文献类型：
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作者：
Benson D
设k是素特征为p的代数闭域，k是有限群G的群代数的块，G具有正规亏群P和阿贝尔惯性商L。然后证明了P与L的某个子群的半直积的群代数的量子化形式上的矩阵代数。要做到这一点，我们首先检查相关的分次代数，使用Jennings-Quillen风格定理。 作为一个例子，我们计算了指数为p阶的超特殊p-群P与中心作用平凡的八阶四元数群的半直积的情况下，非主块的基本代数的伴随阶数.在的情况下，我们给出了明确的生成元和关系的基本代数作为一个量子化的版本。作为第二个例子，我们给出了明确的发电机和关系的情况下，一组形状的特征2。
Let k be an algebraically closed field of prime characteristic p. Let be a block of a group algebra of a finite group G, with normal defect group P and abelian inertial quotient L. Then we show that is a matrix algebra over a quantised version of the group algebra of a semidirect product of P with a certain subgroup of L. To do this, we first examine the associated graded algebra, using a Jennings–Quillen style theorem. As an example, we calculate the associated graded of the basic algebra of the nonprincipal block in the case of a semidirect product of an extraspecial p-group P of exponent p and order with a quaternion group of order eight with the centre acting trivially. In the case of , we give explicit generators and relations for the basic algebra as a quantised version of . As a second example, we give explicit generators and relations in the case of a group of shape in characteristic two.