Abstract
We have seen in the previous chapter that understanding finite-dimensional modules of an algebra reduces to understanding all indecomposable modules. This leads to the concept of representation type. An algebra has finite representation type if it has only finitely many finite-dimensional indecomposable modules up to isomorphism, otherwise it has infinite representation type. After discussing these notions, we determine the representation type for some classes of algebras. In particular, we show that the group algebra of a finite group has finite representation type if and only if the Sylow p-subgroups of the group are cyclic, here p is the characteristic of the coefficient field.
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T.S. Blyth, E.F. Robertson, Further Linear Algebra. Springer Undergraduate Mathematics Series. Springer-Verlag London, Ltd., 2002.
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Erdmann, K., Holm, T. (2018). Representation Type. In: Algebras and Representation Theory. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-91998-0_8
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DOI: https://doi.org/10.1007/978-3-319-91998-0_8
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Online ISBN: 978-3-319-91998-0
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