Abstract
We prove that the description of cubic functors is a wild problem in the sense of the representation theory. On the contrary, we describe several special classes of such functors (2-divisible, weakly alternative, vector spaces and torsion free ones). We also prove that cubic functors can be defined locally and obtain corollaries about their projective dimensions and torsion free parts.
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Acknowledgments
This research was mainly performed when the author was at the Max-Plank-Institut für Mathematik. I am extremely grateful to the Institute for the excellent opportunity and working conditions. I am also grateful to H.-J. Baues who enthusiastically supported this research and to W. Dreckman for useful discussions. This work was supported by the Max-Planck-Institut für Mathematik and by the CRDF Award UM2-2094.