Polynomial Invariants of Five-Dimensional Orthogonal Groups

Polynomial Invariants of Five-Dimensional Orthogonal Groups

黃文彬(Wen-Bin Huang)

指導教授 ： 洪有情

國立臺灣師範大學/理學院/數學系/碩士(2002年)

並列摘要

Let Q be a nondegenerate quadratic form over the nite eld Fq of odd prime power order
q with charFq 6= 2 and Let On(Fq) be the associated orthogonal group. Let On(Fq) act
linearly on the polynomial ring Fq[x1; : : : ; xn]: In this thesis we nd the invariant subring
Fq[x1; x2; x3; x4; x5]O5(Fq ) with explicit generators. We also prove that this subring is a UFD.

參考文獻

[1] M.F. Atyiah and I.G. Macdonald, Introduction to Commutative Algebra. Addison-Wesley Redaing,

Mass., 1969.

[2] D. Carlisle and P. Kropholler, Rational invariants of certain orthogonal and unitary groups. Bull.

London Math. Soc. 24 (1992), 57-60.

[3] L. Chiang and Y. C. Hung, The invariants of orthogonal group actions. Bull. Astralian Math. Soc. 48