Functorial filtrations for homotopy categories of some generalisations of gentle algebras
Raphael Bennett-Tennenhaus

TL;DR
This paper classifies complexes in the homotopy category of certain gentle algebras over a noetherian ring, using functorial filtrations to describe indecomposables and verify their uniqueness.
Contribution
It introduces a functorial filtration approach to classify indecomposable complexes in the homotopy category of generalized gentle algebras over a noetherian ring.
Findings
Complexes with finitely-generated components decompose into string and band complexes.
The classification of indecomposables is achieved using functorial filtrations.
The Krull-Remak-Schmidt-Azumaya property is verified for these categories.
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
