# SAGBI bases in rings of multiplicative invariants

### Zinovy Reichstein

University of British Columbia, Vancouver, Canada

## Abstract

Let k be a field and G be a finite subgroup of $\GL_n(\mathbb Z)$. We show that the ring of multiplicative invariants $k[x_1^{\pm 1}, \dots, x_n^{\pm 1}]^G$ has a finite SAGBI basis if and only if G is generated by reflections.

## Cite this article

Zinovy Reichstein, SAGBI bases in rings of multiplicative invariants. Comment. Math. Helv. 78 (2003), no. 1, pp. 185–202

DOI 10.1007/S000140300008