JournalscmhVol. 78, No. 1pp. 185–202

SAGBI bases in rings of multiplicative invariants

  • Zinovy Reichstein

    University of British Columbia, Vancouver, Canada
SAGBI bases in rings of multiplicative invariants cover
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Abstract

Let k be a field and G be a finite subgroup of \GLn(Z)\GL_n(\mathbb Z). We show that the ring of multiplicative invariants k[x1±1,,xn±1]Gk[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