Classification of modules for infinite-dimensional string algebras

Crawley-Boevey, William

doi:10.1090/tran/7032

Classification of modules for infinite-dimensional string algebras
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by William Crawley-Boevey PDF

Trans. Amer. Math. Soc. 370 (2018), 3289-3313 Request permission

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 modules 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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