关于几乎源代数融合系统的猜想不变性
Conjectural invariance with respect to the fusion system of an almost-source algebra
摘要：
我们表明，给定一个几乎源代数$A$的一个$p$块的有限群$G$，那么单位群的$A$包含一个基础稳定的左，右乘法行动的缺陷组的当且仅当，在某种意义上是精确的，某些相对重局部指向组是不变的融合系统。当$G$是$p$ -可解时，这两个等价条件对给定$p$ -块的几乎源代数成立.一个动机在于这样一个事实，根据Linkelmann的定理，如果两个等价条件对$A$成立，那么任何稳定的基础$A$是半特征的融合系统。
英文摘要：
We show that, given an almost-source algebra $A$ of a $p$-block of a finite group $G$, then the unit group of $A$ contains a basis stabilized by the left and right multiplicative action of the defect group if and only if, in a sense to be made precise, certain relative multiplicities of local pointed groups are invariant with respect to the fusion system. We also show that, when $G$ is $p$-solvable, those two equivalent conditions hold for some almost-source algebra of the given $p$-block. One motive lies in the fact that, by a theorem of Linckelmann, if the two equivalent conditions hold for $A$, then any stable basis for $A$ is semicharacteristic for the fusion system.
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