The n-Homology of Harish-Chandra Modules: Generalizing a Theorem of Kostant.

David H. Collingwood

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In [2] an internal homology theory of crossed modules was defined (CCG-homology for short), which is very much related to the homology of the classifying spaces of crossed modules ([5]). The goal of this note is to construct a low-dimensional homology exact sequence corresponding to a central extension of crossed modules, which is quite similar to the one constructed in [3] for group homology.