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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

SAGBI bases for rings of invariant Laurent polynomials


Authors: Alexander Duncan and Zinovy Reichstein
Journal: Proc. Amer. Math. Soc. 137 (2009), 835-844
MSC (2000): Primary 13A50, 13P99
Published electronically: September 15, 2008
MathSciNet review: 2457421
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ k$ be a field, let $ L_n = k[x_1^{\pm 1}, \dots, x_n^{\pm 1}]$ be the Laurent polynomial ring in $ n$ variables and let $ G$ be a finite group of $ k$-algebra automorphisms of $ L_n$. We give a necessary and sufficient condition for the ring of invariants $ L_n^G$ to have a SAGBI basis. We show that if this condition is satisfied, then $ L_n^G$ has a SAGBI basis relative to any choice of coordinates in $ L_n$ and any term order.


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Additional Information

Alexander Duncan
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Email: duncan@math.ubc.ca

Zinovy Reichstein
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Email: reichst@math.ubc.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09538-5
PII: S 0002-9939(08)09538-5
Keywords: SAGBI basis, subduction algorithm, G\"obel's conjecture, group action, algebra of invariants, reflection group, abelian semigroup
Received by editor(s): February 6, 2008
Received by editor(s) in revised form: February 28, 2008
Published electronically: September 15, 2008
Additional Notes: The first author was partially supported by an NSERC Canada Graduate Scholarship.
The second author was partially supported by NSERC Discovery and Accelerator Supplement grants
Communicated by: Martin Lorenz
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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