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Does the Automorphism Group Generate the Endomorphism Ring in Rep(S, R)?

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
231
Issue
1
Identifiers
DOI: 10.1006/jabr.2000.8361

Abstract

Abstract Let R be a principal ideal domain and let (S,≤) be a finite poset. We consider the question whether the automorphism group of a representation V∈Rep(S,R) generates the endomorphism ring of V. A complete solution is given if R=k is a field except in the case of GF(2). Moreover, some partial results and helpful techniques are obtained for the general case of R being a principal ideal domain, not a field.

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