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Given a scalar parameter $q$, the $q$-deformed Heisenberg algebra$\mathcal{H}(q)$ is the unital associative algebra with two generators $A,B$that satisfy the $q$-deformed commutation relation $AB-qBA= I$, where $I$ isthe multiplicative identity. For $\mathcal{H}(q)$ of torsion-type, that is if$q$ is a root of unity, characterization is obtained for all the Liepolynomials in $A,B$ and basis and graded structure and commutation relationsfor associated Lie algebras are studied.

Torsion-type $q$-deformed Heisenberg algebra and its Lie polynomials