Derived Categories of Nodal Algebras

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In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known algebras as the complete ring of a double nodal point [[x,y]]/(xy) and the completed path algebra of the Gelfand quiver. As a corollary we obtain a description of the derived category of Harish-Chandra modules over SL₂(R). We also give an algorithm, which allows to construct projective resolutions of indecomposable complexes. In the appendix we prove the Krull-Schmidt theorem for homotopy categories.