caa a22 4500 445835737 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-010-0663-z doi (NATIONALLICENCE)springer-10.1007/s00209-010-0663-z Extended canonical algebras and Fuchsian singularities [Elektronische Daten] [Helmut Lenzing, José de la Peña] The authors introduce a new class of finite dimensional algebras called extended canonical, and determine the shape of their derived categories. Extended canonical algebras arise from a canonical algebra Λ by onepoint extension or coextension by an indecomposable projective module. Our main results concern the case of negative Euler characteristic of the corresponding weighted projective line $${\mathbb{X}}$$; more specifically we establish, for a base field of arbitrary characteristic, a link to the Fuchsian singularity R of $${\mathbb{X}}$$ which for the base field of complex numbers is isomorphic to an algebra of automorphic forms. By means of a recent result of Orlov we show that the triangulated category of the graded singularities of R (in the sense of Buchweitz and Orlov) admits a tilting object whose endomorphism ring is the corresponding extended canonical algebra. Of particular interest are those cases where the attached Coxeter transformation has spectral radius one. A K-theoretic analysis then shows that this happens exactly for 38 cases including Arnold's 14 exceptional unimodal singularities. The paper is related to recent independent work by Kajiura, Saito and Takahashi. Springer-Verlag, 2010 Lenzing Helmut Institut für Mathematik, Universität Paderborn, 33095, Paderborn, Germany aut de la Peña José Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, Mexico, DF, Mexico aut Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 143-167 0025-5874 268:1-2<143 2011 268 209 https://doi.org/10.1007/s00209-010-0663-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0663-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lenzing Helmut Institut für Mathematik, Universität Paderborn, 33095, Paderborn, Germany aut NATIONALLICENCE 700 1- de la Peña José Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, Mexico, DF, Mexico aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 143-167 0025-5874 268:1-2<143 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer