论文标题
在dales-zelazko猜想中，用于离散组的代数
On the Dales-Zelazko conjecture for Beurling algebras on discrete groups
论文作者
论文摘要
让$ g $是几乎可溶的或几乎免费的集团，让$ω$为$ g $的权重。我们证明，如果$ g $是无限的，那么在beurling代数$ \ ell^1（g，ω）$中，有限的codimension的最大理想是（代数）生成的。这意味着，这些BANACH代数的猜想和Zelazko的猜想。然后，我们继续提供加权群体的例子，该属性以强大的方式失败。例如，我们描述了一个无限群体上的beurling代数，其中每个有限的codimensionsimension的左侧理想都是有限生成的，并且在残留有限的维度方面具有许多这样的理想。这些例子似乎很难证明Dales和Zelazko的猜想。
Let $G$ be a group which is either virtually soluble or virtually free, and let $ω$ be a weight on $G$. We prove that, if $G$ is infinite, then there is some maximal left ideal of finite codimension in the Beurling algebra $\ell^1(G, ω)$ which fails to be (algebraically) finitely generated. This implies that a conjecture of Dales and Zelazko holds for these Banach algebras. We then go on to give examples of weighted groups for which this property fails in a strong way. For instance we describe a Beurling algebra on an infinite group in which every left ideal of finite codimension is finitely generated, and which has many such ideals in the sense of being residually finite dimensional. These examples seem to be hard cases for proving Dales and Zelazko's conjecture.
