论文标题
关于组代数的理想：不确定性原理和Schur产品
On ideals in group algebras: an uncertainty principle and the Schur product
论文作者
论文摘要
在本文中，我们研究了有限群体的组代数组中理想的某些特性。首先，我们重点介绍了它们的尺寸，最小锤距离和小组顺序之间的重要联系。这是Meshulam在1992年显示的不确定性原理的广义版本。其次，我们介绍了组代数中理想的Schur乘积的概念，并研究了Schur正方形的模块结构和尺寸。我们对与其Schur广场一致的理想给出结构性结果，并提供了一个理想的条件，以使其Schur Square具有琐事模块的投射覆盖，作为直接求和。这对于特征p领域的p组组代数群会产生特别有趣的后果。
In this paper we investigate some properties of ideals in group algebras of finite groups over fields. First, we highlight an important link between their dimension, their minimal Hamming distance and the group order. This is a generalized version of an uncertainty principle shown in 1992 by Meshulam. Secondly, we introduce the notion of the Schur product of ideals in group algebras and investigate the module structure and the dimension of the Schur square. We give a structural result on ideals that coincide with their Schur square, and we provide conditions for an ideal to be such that its Schur square has the projective cover of the trivial module as a direct summand. This has particularly interesting consequences for group algebras of p-groups over fields of characteristic p.
