Rank varieties for a class of finite-dimensional local algebras |
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Authors: | David J Benson |
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Institution: | a Department of Mathematical Sciences, University of Aberdeen, Meston Building, King’s College, Aberdeen AB24 3UE, UK b Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, UK |
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Abstract: | We develop a rank variety for finite-dimensional modules over a certain class of finite-dimensional local k-algebras, . Included in this class are the truncated polynomial algebras , with k an algebraically closed field and arbitrary. We prove that these varieties characterise projectivity of modules (Dade’s lemma) and examine the implications for the tree class of the stable Auslander-Reiten quiver. We also extend our rank varieties to infinitely generated modules and verify Dade’s lemma in this context. |
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Keywords: | Primary 16G10 16D40 secondary 16S35 16S38 |
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