Abstract
We give a description of matrix bimodules parametrizing all indecomposable homogeneous Λ-modules with a fixed integral slope over a tubular canonical algebra Λ, for all possible integers (Theorem 4.1). An important role in the first step of this description (Theorem 2.4) is played by the translation of the shift functor for coherent sheaves over the associated weighted projective line to the language of Λ-modules (Theorem 3.2).
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Piotr Dowbor and Andrzej Mróz are supported by the Research Grant N N201 542138 of the Polish Ministry of Science and Higher Education.
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Dowbor, P., Meltzer, H. & Mróz, A. Parametrizations for Integral Slope Homogeneous Modules over Tubular Canonical Algebras. Algebr Represent Theor 17, 321–356 (2014). https://doi.org/10.1007/s10468-012-9386-7
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DOI: https://doi.org/10.1007/s10468-012-9386-7
Keywords
- Parametrizing bimodule
- Homogeneous module
- Canonical tubular algebra
- Weighted projective line
- Coherent sheaf
- Derived category
- ξ-matrix
- Quasi-diagonal form