Classification of modules for infinite-dimensional string algebras

2013/08/29 by William Crawley-Boevey, Crawley-Boevey, William · 4 citations
Mathematics · #13C05 (Secondary) #16D70 (Primary) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:13C05 #msc:16D70

paper · pdf · doi:10.48550/arxiv.1308.6410

Corrected and substantially revised, it now also includes the classification of artinian modules

arxiv created 2016/03/04 · arxiv updated 2016/03/07

Abstract

We relax the definition of a string algebra to also include infinite-dimensional algebras such as k[x,y]/(xy). Using the functorial filtration method, which goes back to Gelfand and Ponomarev, we show that finitely generated and artinian modules (and more generally finitely controlled and pointwise artinian modules) are classified in terms of string and band modules. This subsumes the known classifications of finite-dimensional modules for string algebras and of finitely generated modules for k[x,y]/(xy). Unlike in the finite-dimensional case, the words parameterizing string modules may be infinite.

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