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arXiv · 2511.16638

Commuting maps on the Heisenberg algebra

Jordan Bounds·Ellis Edinkrah
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Abstract

Given a ring $R$ with center $Z(R)$, we say a linear map $f:R\rightarrow R$ is commuting if $[f(x),x]=0$ for all $x\in R$. Such a map has a standard form if there exists $\lambda\in R$ and additive $\mu:R\rightarrow Z(R)$ such that $f(x)=\lambda x+\mu(x)$ for all $x\in R$. We characterize the linear commuting maps over the $n\times n$ Heisenberg algebra, showing that such maps need not be of the standard form.

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Jordan Bounds, Ellis Edinkrah. 2025-11-20. Commuting maps on the Heisenberg algebra. https://arxiv.org/abs/2511.16638

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