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arXiv · 1608.08514

Functorial filtrations for homotopy categories of some generalisations of gentle algebras

Raphael Bennett-Tennenhaus
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Abstract

We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with finitely-generated homogeneous components are shown to be isomorphic to direct sums of indecomposable string and band complexes. The corresponding isoclasses are described, and the Krull-Remak-Schmidt-Azumaya property is verified. This classification problem is solved using the idea of functorial filtrations.

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BibTeXRIS

Raphael Bennett-Tennenhaus. 2016-08-30. Functorial filtrations for homotopy categories of some generalisations of gentle algebras. https://arxiv.org/abs/1608.08514

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