We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm112-1-3, author = {Grzegorz Bobi\'nski and Piotr Malicki}, title = {On derived equivalence classification of gentle two-cycle algebras}, journal = {Colloquium Mathematicae}, volume = {111}, year = {2008}, pages = {33-72}, zbl = {1148.18006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm112-1-3} }
Grzegorz Bobiński; Piotr Malicki. On derived equivalence classification of gentle two-cycle algebras. Colloquium Mathematicae, Tome 111 (2008) pp. 33-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm112-1-3/