Geodesic
Irreducible Modules for Polycyclic Group Algebras
Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 901-914

Voir la notice de l'article provenant de la source Cambridge University Press

If G is a polycyclic group and k an absolute field then every irreducible kG-module is finite dimensional [10], while if k is nonabsolute every irreducible module is finite dimensional if and only if G is abelian-by-finite [3]. However something more can be said about the infinite dimensional irreducible modules. For example P. Hall showed that if G is a finitely generated nilpotent group and V an irreducible kG-module, then the image of kZ in EndkG V is algebraic over k [3]. Here Z = Z(G) denotes the centre of G. It follows that the restriction Vz of V to Z is generated by finite dimensional kZ-modules. In this paper we prove a generalization of this result to polycyclic group algebras.We introduce some terminology. 
Musson, I. M. Irreducible Modules for Polycyclic Group Algebras. Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 901-914. doi: 10.4153/CJM-1981-071-1
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