Picard groups of multiplicative invariants | Zendy

Martin Lorenz | Zendy

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Picard groups of multiplicative invariants

Author(s) -

Martin Lorenz

Publication year - 1997

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050023

Subject(s) - mathematics , multiplicative function , picard group , abelian group , multiplicative group , pure mathematics , finitely generated abelian group , torsion (gastropod) , algebra over a field , group (periodic table) , group algebra , combinatorics , medicine , mathematical analysis , chemistry , surgery , organic chemistry

. 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 = S G . As an application, we produce new polycyclic group algebras with nontrivial torsion in K 0 .

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