Abstract
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 present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.
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Lorenz, M. Multiplicative Invariants and Semigroup Algebras. Algebras and Representation Theory 4, 293–304 (2001). https://doi.org/10.1023/A:1011415025465
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DOI: https://doi.org/10.1023/A:1011415025465