Homological algebra with locally compact abelian groups
Copyright policy )Homological algebra with locally compact abelian groups
In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a natural tensor product and internal Hom which both admit derived versions.
18 pages, AMSLaTeX
- University of Göttingen Germany
Mathematics(all), Mathematics - Number Theory, LCA group, tensor product, Mathematics - Category Theory, General properties and structure of LCA groups, Group Theory (math.GR), Resolutions; derived functors (category-theoretic aspects), Internal Hom, 22B05 (Primary) 18G10 (Secondary), Derived Hom-functor, Tensor product, derived hom-functor, FOS: Mathematics, Category Theory (math.CT), internal hom, Number Theory (math.NT), Mathematics - Group Theory
Mathematics(all), Mathematics - Number Theory, LCA group, tensor product, Mathematics - Category Theory, General properties and structure of LCA groups, Group Theory (math.GR), Resolutions; derived functors (category-theoretic aspects), Internal Hom, 22B05 (Primary) 18G10 (Secondary), Derived Hom-functor, Tensor product, derived hom-functor, FOS: Mathematics, Category Theory (math.CT), internal hom, Number Theory (math.NT), Mathematics - Group Theory
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