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action on the cohomology of a rank two abelian group with arbitrary coefficient domain
Authors:Eric Jespers   Alexander Zimmermann
Affiliation:Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium ; LAMFA, Faculté de Mathématiques, Université de Picardie Jules Verne, 33 rue St Leu, 80039 Amiens Cedex, France
Abstract:

A rank two abelian group $C_ntimes C_n$ is in a natural way an $SL_2({mathbb Z})$-module. This induces an action of $SL_2({mathbb Z})$ on its group cohomology $H^m(C_ntimes C_n,R)$ for any trivial coefficient domain $R$. In the present note we determine this module, including the question of when the universal coefficient theorem sequence splits.

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