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.
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Received: March 5, 2002
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Reichstein, Z. SAGBI bases in rings of multiplicative invariants. Comment. Math. Helv. 78, 185–202 (2003). https://doi.org/10.1007/s000140300008
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DOI: https://doi.org/10.1007/s000140300008