Multiplicative Invariants and Semigroup Algebras

Details Multiplicative Invariants and Semigroup Algebras Multiplicative Invariants and Semigroup Algebras

1999-01-26

arxiv.org/abs/math/9901119v1

Mathematics

Commutative Algebra

AMS-LateX, 16 pages, 1 figure

Scientific paper

Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We investigate when algebras of multiplicative invariants are semigroup algebras. In particular, we present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are indeed semigroup algebras. On the other hand, multiplicative invariants arising from fixed point free actions are shown to never be semigroup algebras. In particular, this holds whenever G has odd prime order.

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