The invariants of orthogonal group actions

li Chiang; yu Ching Hung

doi:10.1017/S0004972700015720

The invariants of orthogonal group actions

li Chiang
, yu Ching Hung

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let F_q be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of F_q -automorphisms acting linearly on the rational function field F_q(x₁, …, x_n). We shall prove that the invariant subfield F_q(x₁,…, x_n)^{O(n, Q)} is a purely transcendental extension over F_q for n = 5 by giving a set of generators for it.

Original language	English
Pages (from-to)	313-319
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	48
Issue number	2
DOIs	https://doi.org/10.1017/S0004972700015720
Publication status	Published - 1993 Oct

ASJC Scopus subject areas

General Mathematics

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10.1017/S0004972700015720

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title = "The invariants of orthogonal group actions",

abstract = "Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of Fq -automorphisms acting linearly on the rational function field Fq(x1, …, xn). We shall prove that the invariant subfield Fq(x1,…, xn)O(n, Q) is a purely transcendental extension over Fq for n = 5 by giving a set of generators for it.",

author = "li Chiang and Hung, \{yu Ching\}",

year = "1993",

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AU - Hung, yu Ching

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N2 - Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of Fq -automorphisms acting linearly on the rational function field Fq(x1, …, xn). We shall prove that the invariant subfield Fq(x1,…, xn)O(n, Q) is a purely transcendental extension over Fq for n = 5 by giving a set of generators for it.

AB - Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of Fq -automorphisms acting linearly on the rational function field Fq(x1, …, xn). We shall prove that the invariant subfield Fq(x1,…, xn)O(n, Q) is a purely transcendental extension over Fq for n = 5 by giving a set of generators for it.

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The invariants of orthogonal group actions

Abstract

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