可消么半群位形代数中的极限元
Limit elements in the configuration algebra for a cancellative monoid
摘要：
我们引入了两个预分拆函数函数空间$Ω(Γ,G)$和反级数空间$Ω(P_{Γ,G})$，它们分别与具有有限生成系统$G$及其增长函数$P_{Γ,G}(t)$的可消幺半群$Γ$的Cayley图$(Γ,G)$相关联.在对$(Γ,G)$的适当假设下，我们引入了一个具有$\Z_{\ge0}$ -作用的纤维化$π_Ω:Ω(Γ,G)\to Ω(P_{Γ,G})$等变元，如果它是有限阶的，那么它是传递的.那么，纤维中的预分拆函数之和是两个增长函数$P_{Γ,G}(t)$和$P_{Γ,G}\mathcal{M}(t)$的比例在收敛半径圆上的极点处附加到$(Γ,G)$的留数的线性组合.
英文摘要：
We introduce two spaces $Ω(Γ,G)$ and $Ω(P_{Γ,G})$ of pre-partition functions and of opposite series, respectively, which are associated with a Cayley graph $(Γ,G)$ of a cancellative monoid $Γ$ with a finite generating system $G$ and with its growth function $P_{Γ,G}(t)$. Under mild assumptions on $(Γ,G)$, we introduce a fibration $π_Ω:Ω(Γ,G)\to Ω(P_{Γ,G})$ equivariant with a $\Z_{\ge0}$-action, which is transitive if it is of finite order. Then, the sum of pre-partition functions in a fiber is a linear combination of residues of the proportion of two growth functions $P_{Γ,G}(t)$ and $P_{Γ,G}\mathcal{M}(t)$ attached to $(Γ,G)$ at the places of poles on the circle of the convergent radius.
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