Source Algebras of p-Central Group Extensions
Source Algebras of p-Central Group Extensions
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DOI：
10.1006/jabr.2000.8474
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发表时间：
2001
影响因子：
0.9
通讯作者：
L. Puig
中科院分区：
文献类型：
--
作者：
L. Puig
1.1.设p是素数，k是特征为p的代数闭域，O是具有剩余w x域k的完全离散赋值环.在11，引理7.8中，我们证明了有限群G的块B的源代数的刚性性质，其中亏群P cf.第38章在X 16，在具有P= P-稳定O-基的OP-内部代数类中：我们证明了它在k上的约化确实决定了O上的源代数。在本文中，我们证明了一个更强的唯一性声明，即，粗略地说，即使它的约化通过一个中心p-子群确定的块的源代数。特别是，我们的结果保证了x = x。如果我们知道B cf的Brauer范畴。第47节在16，对于任何
1.1. Let p be a prime number, k an algebraically closed field of characteristic p, and O a complete discrete valuation ring with residue w x field k. In 11, Lemma 7.8, we show the rigid nature of the source algebra Ž of a block b of a finite group G, with defect group P cf. Section 38 in w x. 16, in the class of OP-interior algebras having a P= P-stable O-basis: we prove indeed that its reduction over k determines the source algebra over O. In this paper, we prove a stronger uniqueness statement namely that, roughly speaking, even its reduction via a central p-subgroup determines the source algebra of a block. In particular, our result guarantees Ž w x. that if we know the Brauer category of b cf. Section 47 in 16, for any