(untitled) (European Journal of Pure and Applied Mathematics, 2024)
This study introduces an ample Hausdorff groupoid A times R extracted from an ample Hausdorff groupoid G and a unital commutative ring R; a Hausdorff groupoid D which is the discrete twist over A times R. In the groupoid C*-algebra perspective, when R = C there is an isomorphism between the non-twisted groupoid C*-algebra (C^*(G)) and the twisted groupoid C*-algebra (C^*(A times R;D)). However, in this paper, in a purely algebraic setting, the non-twisted Steinberg algebra (A_R(G)) and the twisted Steinberg algebra (A_R(D; A times R)) are non-isomorphic.