Abstract
In this chapter we provide an account of the theory connecting the category of modules of a finite dimensional algebra A with the module categories of the algebras eAe and A∕AeA, for an idempotent e ∈ A, known as recollement [BBD82, CPS88, CPS96]. We first learned of this subject from the monograph of Green [Gre80, Chapter 6]. A presentation much closer in spirit to ours is that of Kuhn [Kuh94b]. In the next chapter, we shall apply this theory to construct the irreducible representations of a finite monoid and in a later chapter we shall extend the results to finite categories.
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References
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Steinberg, B. (2016). 4 Recollement: The Theory of an Idempotent. In: Representation Theory of Finite Monoids. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-43932-7_4
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DOI: https://doi.org/10.1007/978-3-319-43932-7_4
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