2003/12/16 by Martin Lorenz, Lorenz, Martin
Mathematics · #13A50 #13C14 #13H10 #16W22 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:13A50 #msc:13C14 #msc:13H10 #msc:16W22
paper · pdf · doi:10.48550/arxiv.math/0312302
16 pages, LaTeX; some new results and examples added; expanded introduction with additional references
openalex publication_date 2003/12/16 · arxiv created 2004/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group G. By definition, these are G-actions on Laurent polynomial algebras that stabilize the multiplicative group consisting of all monomials in the variables. For the most part, we concentrate on the case where the base ring is the ring of rational integers. Our main result states that if G acts non-trivially and the invariant algebra is Cohen-Macaulay then the abelianized isotropy groups Gm/[Gm,Gm] of all monomials m are generated by bireflections and at least one Gm/[Gm,Gm] is non-trivial. As an application, we prove the multiplicative version of Kemper's 3-copies conjecture.