论文标题
具有正常缺陷和Abelian $ p'$惯性商的块的结构
Structure of blocks with normal defect and abelian $p'$ inertial quotient
论文作者
论文摘要
让$ k $为主要特征$ p $的代数封闭场。让$ kge $是有限组$ g $的组代数的一个块，有正常的缺陷组$ p $和abelian $ p'$惯性商$ l $。然后，我们表明$ kge $是矩阵代数，比$ p $的$ p $的组代数的量化版本具有$ l $的某个子组。为此，我们首先使用詹宁斯（Jennings） - Quillen Style定理研究相关的分级代数。 例如，我们计算非主要块的基本代数的相关分级，如果是外部$ p $ -p $ -group $ p $ oftement $ p $ $ p $和订单$ p^3 $的半领产品，其中Quaternion of quaternion of Quaternion of quaternion of Quaternion of ose of八订单，中心表现得很琐碎。在情况下，在$ p = 3 $的情况下，我们将基本代数的显式发电机和关系作为$ kp $的量化版本。作为第二个示例，在特征两个中，我们给出了明确的生成器和关系，如果一组形状$ 2^{1+4}：3^{1+2} $。
Let $k$ be an algebraically closed field of prime characteristic $p$. Let $kGe$ be a block of a group algebra of a finite group $G$, with normal defect group $P$ and abelian $p'$ inertial quotient $L$. Then we show that $kGe$ 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 non-principal block in the case of a semidirect product of an extraspecial $p$-group $P$ of exponent $p$ and order $p^3$ with a quaternion group of order eight with the centre acting trivially. In the case $p=3$ we give explicit generators and relations for the basic algebra as a quantised version of $kP$. As a second example, we give explicit generators and relations in the case of a group of shape $2^{1+4}:3^{1+2}$ in characteristic two.
