Picard groups of multiplicative invariants

  • Martin Lorenz

    Temple University, Philadelphia, USA


Let S = kA denote the group algebra of a finitely generated free abelian group A over the field k and let G be a finite subgroup of GL(A). Then G acts on S by means of the unique extension of the natural GL(A)-action on A. We determine the Picard group Pic R of the algebra of invariants R = SG. As an application, we produce new polycyclic group algebras with nontrivial torsion in K0.

Cite this article

Martin Lorenz, Picard groups of multiplicative invariants. Comment. Math. Helv. 72 (1997), no. 3, pp. 389–399

DOI 10.1007/S000140050023