Variations on a Casselman–Osborne Theme

  • Dragan MiličićEmail author
Part of the Developments in Mathematics book series (DEVM, volume 38)


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 words

Derived functors Centers of categories Casselman–Osborne lemma Wigner lemma 

Mathematics Subject Classification (2010):

Primary 16E35 Secondary 22E47. 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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