Iterative Algebras
Iterative Algebras
复制标题
迭代代数
DOI：
10.1007/s10468-015-9550-y
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发表时间：
2015
影响因子：
0.6
通讯作者：
Blake Madill
中科院分区：
文献类型：
--
作者：
J. Bell;Blake Madill
给出一个有限生成的自由么半群X和一个态射ϕ：X→X，我们证明了可以自然地构造一个代数，我们称之为迭代代数。我们证明了迭代代数的许多环论性质可以很容易地用线性代数和态射的组合数据来刻画，而且，迭代代数是否具有这些性质是可判定的。最后，我们利用我们的构造来回答Greenfeld，Leroy，Smoktunowicz和ZiemBowski的几个问题，构造了一个有限生成的Gelfand-Kirillov维本原分次幂零代数。
Given a finitely generated free monoid X and a morphism ϕ : X → X, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras can be easily characterized in terms of linear algebra and combinatorial data from the morphism and that, moreover, it is decidable whether or not an iterative algebra has these properties. Finally, we use our construction to answer several questions of Greenfeld, Leroy, Smoktunowicz, and Ziembowski by constructing a primitive graded nilpotent algebra with Gelfand-Kirillov dimension two that is finitely generated as a Lie algebra.