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arXiv · 2202.05225

On the Identity Problem for Unitriangular Matrices of Dimension Four

Ruiwen Dong
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Abstract

We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group $\mathsf{UT}(4, \mathbb{Z})$ of $4 \times 4$ unitriangular integer matrices. As a byproduct of our proof, we also show the polynomial-time decidability of several subset reachability problems in $\mathsf{UT}(4, \mathbb{Z})$.

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Ruiwen Dong. 2022-02-10. On the Identity Problem for Unitriangular Matrices of Dimension Four. https://arxiv.org/abs/2202.05225

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