On derived equivalence classification of gentle two-cycle algebras

Abstract

N) Abstract. We classify, up to derived (equivalently, tilting-cotil- ting) equivalence all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case. Introduction and the main result Throughout the paper k denotes a fixed algebraically closed field. By an algebra we mean a finite dimensional basic connected k-algebra and by a module a finite dimensional left module. By Z, N, and N+, we denote the sets of integers, nonnegative integers, and positive integers, respectively. Finally, if i, j ∈ Z, then (i, j) = {l ∈ Z | i ≤ l ≤ j}. With an algebrawe may associate its bounded derived category D b (�) (in the sense of Verdier (29)) of bounded complexes of �-modules,