In the second part of this paper, we use the theory described in the first part to construct an example of a counterintuitive phenomenon. We show how to produce examples of filtered systems in the stable module category stmod(kG) which do not lift to filtered systems in the module category mod(kG). Our main tool is the Extended Milnor Sequence, a five-term exact sequence which specializes to the classical Milnor sequence under certain countability conditions.
- phantom maps
- modular representation theory
- extended Milnor sequence