Finite SAGBI bases for polynomial invariants of conjugates of alternating groups期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Finite SAGBI bases for polynomial invariants of conjugates of alternating groups

Authors:	Manfred Gö bel.

Affiliation:	Dettenbachstraß{}e 16, 94154 Neukirchen vorm Wald, Germany

Abstract:	It is well-known, that the ring $mathbb{C} [X_1,dotsc,X_n]^{A_n}$ of polynomial invariants of the alternating group has no finite SAGBI basis with respect to the lexicographical order for any number of variables . 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 with respect to , has a finite SAGBI basis for any .

Keywords:	Algorithmic invariant theory finite SAGBI bases alternating groups rewriting techniques

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