Indecomposable Objects in Derived Categories via the Category of Triples
A reduction technique that classifies the indecomposable objects of the derived category of a semi-perfect associative algebra A by embedding A into a larger algebra with the same radical and translating complexes into triples (a complex over the larger algebra, a complex over the semisimple quotient, and a gluing morphism). The resulting classification becomes a matrix problem - a bunch of chains or of semi-chains - and the method applies to gentle algebras, skew-gentle algebras including those of infinite homological dimension, and the degenerated tubular algebra of type (2,2,2,2;0), which is shown to be derived-tame of exponential growth.
Indecomposables of the derived categories of certain associative algebras
Igor Burban (Kaiserslautern, Kyiv University and the Institute of Mathematics) and Yurij Drozd (Kyiv Taras Shevchenko University and Kaiserslautern), arXiv math/0307062v1, math.RT and math.RA, July 2…