An explicit non-elementary matrix over a bivariate Laurent polynomial ring

Vasiliy Ionin; Artem Semidetnov

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arXiv · 2609.04275

An explicit non-elementary matrix over a bivariate Laurent polynomial ring

Vasiliy Ionin·Artem Semidetnov

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Abstract

Let $F$ be the fraction field of a discrete valuation ring. We give an explicit matrix in $\mathrm{SL}_2(F[X^{\pm1},Y^{\pm1}])\setminus \mathrm{E}_2(F[X^{\pm1},Y^{\pm1}])$. The proof of non-elementarity is based on techniques developed by Peter Abramenko in his preprint arXiv:0808.1095v1.

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Vasiliy Ionin, Artem Semidetnov. 2026-09-02. An explicit non-elementary matrix over a bivariate Laurent polynomial ring. https://arxiv.org/abs/2609.04275

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