Polytopal linear groups (Anton Shafarevich)

Let P ⊆ R^n be a lattice polytope; i.e., P is a convex hull of a finite subset of Z^n ⊆ R^n. Consider the subsemigroup S_P in Z^{n+1} generated by the set {(x; 1)| x ∈ P∩Z^n}. The polytopal algebra associated with P is the semigroup algebra k[S_P] where k is a field. The algebra k[S_P] is naturally graded by the group Z. Following the work of Winfried Bruns and Joseph Gubeladze we will give a description of the group of graded automorphisms of k[S_P].

References:
[1] Winfried Bruns and Joseph Gubeladze. Polytopal linear groups. Journal of Algebra 218, 715-737 (1999)