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arXiv · 1812.06757

An extension of a $q$-deformed Heisenberg algebra and its Lie polynomials

Rafael Reno S. Cantuba·Mark Anthony C. Merciales
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Abstract

Let $\mathbb{F}$ be a field, and fix a $q\in\mathbb{F}$. The $q$-deformed Heisenberg algebra $\mathcal{H}(q)$ is the unital associative algebra over $\mathbb{F}$ with generators $A$, $B$ and a relation which asserts that $AB - qBA$ is the multiplicative identity in $\mathcal{H}(q)$. We extend $\mathcal{H}(q)$ into an algebra $\mathcal{R}(q)$ defined by generators $A$, $B$ and a relation which asserts that $AB-qBA$ is central in $\mathcal{R}(q)$. We identify all elements of $\mathcal{R}(q)$ that are Lie polynomials in $A$, $B$.

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Rafael Reno S. Cantuba, Mark Anthony C. Merciales. 2018-12-17. An extension of a $q$-deformed Heisenberg algebra and its Lie polynomials. https://doi.org/10.1016/j.exmath.2019.12.001

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