Modular Invariant Theory pp 185-189 | Cite as

# Rings of Invariants which are Hypersurfaces

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## Abstract

As we have seen, we seek to characterize those representations *V* of groups *G* whose rings of invariants are well-behaved. The best behaved rings of invariants, \(\mathbb{K}[V]^{G}\), are those which are polynomial rings, that is, \(\mathbb{K}[V]^{G}\) is generated by dim (*V*) many invariants. A slightly less well behaved class of examples is provided by those rings of invariants which are hypersurfaces, that is, \(\mathbb{K}[V]^{G}\) is generated by dim (*V*)+1 many invariants. Those representations with this property have been extensively studied in characteristic 0 by Nakajima (1983). Less is known for modular groups. When *G* is a Nakajima group with maximal proper subgroup *H*, the following proposition shows that the ring of *H*-invariants is a hypersurface (or a polynomial) ring.

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## References

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*Rings of invariants of finite groups which are hypersurfaces*, J. Algebra**80**(1983), no. 2, 279–294. MR 85e:20036 zbMATHCrossRefMathSciNetGoogle Scholar