Abstract
The theoretical background of the TUBULAR package, developed for a computer algebra treatment of sheaves over weighted projective (tubular) lines is presented. The package is also of interest for classifying indecomposable modules over finite dimensional tubular algbras, resp. G-equivariant sheaves over elliptic curves with respect to certain actions of finite groups. The encoding of indecomposable sheaves by a set of discrete data (using the tubular structure of coh X) and the effective method of determining the class [\(\mathcal{F}\)] of indecomposable \(\mathcal{F} \in coh \mathbb{X}\) in the Grothendieck group \({{K}_{0}}\mathbb{X}\) (based on the telescoping functor technique) are explained. Certain additional facts improving efficiency of this method are discussed.
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Dowbor, P., Hübner, T. (1999). A Computer Algebra Approach to sheaves over Weighted Projective Lines. In: Dräxler, P., Ringel, C.M., Michler, G.O. (eds) Computational Methods for Representations of Groups and Algebras. Progress in Mathematics, vol 173. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8716-8_10
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DOI: https://doi.org/10.1007/978-3-0348-8716-8_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9740-2
Online ISBN: 978-3-0348-8716-8
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