On the Identity Problem for Unitriangular Matrices of Dimension Four

02/10/2022

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by   Ruiwen Dong, et al.

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