### Abstract

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.

Original language | English |
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Pages (from-to) | 395-404 |

Number of pages | 9 |

Journal | Algebras and Representation Theory |

Volume | 4 |

DOIs | |

Publication status | Published - 2001 |

### Keywords

- phantom maps
- modular representation theory
- extended Milnor sequence

## Cite this

Benson, D. J., & Gnacadja, D. G. P. (2001). Phantom maps and purity in modular representation theory, II.

*Algebras and Representation Theory*,*4*, 395-404. https://doi.org/10.1023/A:1012475019810