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arXiv · 1309.1237

On Lower Central Series Quotients of Finitely Generated Algebras over $\mathbb{Z}$

Katherine Cordwell·Teng Fei·Kathleen Zhou
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Abstract

Let $A$ be an associative unital algebra, $B_k$ its successive quotients of lower central series and $N_k$ the successive quotients of ideals generated by lower central series. The geometric and algebraic aspects of $B_k$ and $N_k$ have been of great interest since the pioneering work of \cite{feigin2007}. In this paper, we will concentrate on the case where $A$ is a noncommutative polynomial algebra over $\mathbb{Z}$ modulo a single homogeneous relation. Both the torsion part and the free part of $B_k$ and $N_k$ are explored. Many examples are demonstrated in detail, and several general theorems are proved. Finally we end up with an appendix about the torsion subgroups of $N_k(A_n(\mathbb{Z}))$ and some open problems.

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Katherine Cordwell, Teng Fei, Kathleen Zhou. 2014-11-25. On Lower Central Series Quotients of Finitely Generated Algebras over $\mathbb{Z}$. https://doi.org/10.1016/j.jalgebra.2014.10.018

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