Variations on a Casselman–Osborne Theme
We discuss two classical results in homological algebra of modules over an enveloping algebra – lemmas of Casselman–Osborne and Wigner. They have a common theme: they are statements about derived functors. While the statements for the functors itself are obvious, the statements for derived functors are not and the published proofs were completely different from each other. First we give simple, pedestrian arguments for both results based on the same principle. Then we give a natural generalization of these results in the setting of derived categories.
Key wordsDerived functors Centers of categories Casselman–Osborne lemma Wigner lemma
Mathematics Subject Classification (2010):Primary 16E35 Secondary 22E47.
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