We show that the Identity Problem is decidable for finitely generated sub-semigroups of the group $\operatorname{UT}(4, \mathbb{Z})$ of $4 \times 4$ unitriangular integer matrices. As a byproduct of our proof, we have also shown the decidability of several subset reachability problems in $\operatorname{UT}(4, \mathbb{Z})$.
翻译:我们显示身份问题对于一个组的有限产生的子小组 $\ operatorname{UT}( 4,\ mathbb}) (4, \ mathbb}) $ 4\ times 4$ unitrialgrongnal 矩阵是可判分的。 作为我们证据的副产品, 我们还用$\ operatorname{UT} (4,\ mathbb}) 来显示几个子子可达性问题的可判分性 。