On commutative invariants for modules over crossed products of minimax nilpotent linear groups

2025/08/17 by Tushev, Anatolii V.
#11R27 #16S34 #20C07 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.12517

Abstract

Let N be a minimax nilpotent torsion-free normal subgroup of a soluble group G of finite rank, R be a finitely generated commutative domain and R*N be a crossed product of R and N. In the paper we construct a correspondence between an R*N-module W and a finite set M of equivalent classes of prime ideals minimal over Ann_kA(W/WI), where kA is a group algebra of an abelian minimax group A and I is an appropriative G-invariant ideal of RG. It is shown that if Wg ≅ W for all g ∈ g then the action of the group G by conjugations on N can be extended to an action of the group G on the set M. The results allow us to apply methods of commutative algebra to the study of W.

Citations

• Irreducible representations of certain nilpotent groups of finite rank
• Primitive irreducible representations of finitely generated nilpotent groups

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