Affiliations: [a] Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland. dowbor@mat.umk.pl | [b] Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Maison du Nombre, 6, Avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg. yan.kim@uni.lu
Correspondence:
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Address for correspondence: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland.
Abstract: The effective method (based on Theorem 5.3) of classifying tubular algebras by the Cartan matrices of tilting sheaves over weighted projective lines with all indecomposable direct summands in some finite “fundamental domain” , by the reduction to the two elementary problems of discrete mathematics having algorithmic solutions is presented in details (see Problem A and B). The software package CART_TUB being an implementation of this method yields the precise classification of all up to isomorphism tubular algebras of a fixed tubular type p, by creating the complete lists of their Cartan matrices, and furnish their tilting realizations. In particular, the number of isomorphism classes of tubular algebras of the type p is determined (Theorem 2.3).
