A Rigidity Property for the Set of all Characters Induced by Valuations

If K is a field and G a finitely generated multiplicative subgroup of K then every real valuation on K induces a character G → R. It is known that the set$\Delta(G) \subseteq R^n$of all characters induced by valuations is polyhedral. We prove that Δ(G) satisfies a certain rigidity property and apply...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1986, Vol.294 (2), p.425-434
Main Authors: Bieri, Robert, John R. J. Groves
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Cartesianism
Concavity
Half spaces
Linear transformations
Mathematical theorems
Mathematical vectors
Polyhedrons
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Summary:If K is a field and G a finitely generated multiplicative subgroup of K then every real valuation on K induces a character G → R. It is known that the set$\Delta(G) \subseteq R^n$of all characters induced by valuations is polyhedral. We prove that Δ(G) satisfies a certain rigidity property and apply this to give a new and conceptual proof of the Brewster-Roseblade result [4] on the group of automorphisms of K stabilizing G.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-1986-0825713-6