Invariant maximal ideals in group algebras
Abstract: Given a finitely generated torsion free abelian group , any group of automorphisms of extends to a group of algebra automorphisms of the group ring . When the automorphism group is cyclic, Roseblade has proved that has infinitely many invariant maximal ideals. We count these ideals with a localized generating function which turns out to be rational.
-  Daniel R. Farkas, Toward multiplicative invariant theory, Group actions on rings (Brunswick, Maine, 1984) Contemp. Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 69–80. MR 810644, https://doi.org/10.1090/conm/043/810644
-  J. E. Roseblade, Group rings of polycyclic groups, J. Pure Appl. Algebra 3 (1973), 307–328. MR 0332944, https://doi.org/10.1016/0022-4049(73)90034-0
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Keywords: Group algebra, characters, matrices over a finite ring
Article copyright: © Copyright 1986 American Mathematical Society