Abstract
The Auslander-Reiten Theorem can be translated into a combinatorial technique called knitting. It yields in many concrete cases large parts or all of the Auslander-Reiten quiver including the structure of the contained indecomposable modules. The development of the knitting technique takes up the main part of this chapter and will exhibited at concrete examples. It underlines the importance of combinatorial invariants, which will be studied with more detail in the next chapter. At the end an example will be discussed, which shows that the technique is not universal and exhibits how it may fail.
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References
Bongartz, K., Gabriel, P.: Covering spaces in representation-theory. Invent. Math. 65, 331–378 (1982)
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Barot, M. (2015). Knitting. In: Introduction to the Representation Theory of Algebras. Springer, Cham. https://doi.org/10.1007/978-3-319-11475-0_7
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DOI: https://doi.org/10.1007/978-3-319-11475-0_7
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