### 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 |
---|---|

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

*Algebras and Representation Theory*,

*4*, 395-404. https://doi.org/10.1023/A:1012475019810

**Phantom maps and purity in modular representation theory, II.** / Benson, David John; Gnacadja, D. G. P.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Phantom maps and purity in modular representation theory, II

AU - Benson, David John

AU - Gnacadja, D. G. P.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - phantom maps

KW - modular representation theory

KW - extended Milnor sequence

U2 - 10.1023/A:1012475019810

DO - 10.1023/A:1012475019810

M3 - Article

VL - 4

SP - 395

EP - 404

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

ER -