Finite dimensional modules and perpendicular subcategories

Mathematics – Representation Theory

Scientific paper

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5 pages, expanding on a construction from the author's PhD thesis

Scientific paper

We explain how, under some hypotheses, one can construct a sequence of finite
dimensional $kG$-modules that lie in certain prescribed additive subcategories,
but whose direct limits do not. We use these to show that many of the
triangulated quotients of $\Mod$ are not generated, as triangulated categories,
by the corresponding quotient of $\mod$ considered as a full subcategory.

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