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Finite SAGBI bases for polynomial invariants of conjugates of alternating groups

Author: Manfred Göbel
Journal: Math. Comp. 71 (2002), 761-765
MSC (2000): Primary 13A50, 12Y05; Secondary 20B35, 14Q99
Published electronically: October 25, 2001
MathSciNet review: 1885626
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Abstract: It is well-known, that the ring $\mathbb{C} [X_1,\dotsc,X_n]^{A_n}$ of polynomial invariants of the alternating group $A_n$ has no finite SAGBI basis with respect to the lexicographical order for any number of variables $n \ge 3$. This note proves the existence of a nonsingular matrix $\delta_n \in GL(n,\mathbb{C} )$ such that the ring of polynomial invariants $\mathbb{C} [X_1,\dotsc,X_n]^{A_n^{\delta_n}}$, where $A_n^{\delta_n}$ denotes the conjugate of $A_n$ with respect to $\delta_n$, has a finite SAGBI basis for any $n \geq 3$.

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Additional Information

Manfred Göbel
Affiliation: Dettenbachstraße 16, 94154 Neukirchen vorm Wald, Germany

Keywords: Algorithmic invariant theory, finite SAGBI bases, alternating groups, rewriting techniques
Received by editor(s): September 7, 1999
Received by editor(s) in revised form: July 19, 2000
Published electronically: October 25, 2001
Article copyright: © Copyright 2001 American Mathematical Society