### Abstract

We associate with any p-block of a finite group a Grothendieck ring of certain p-permutation bimodules. We extend the notion of p-permutation equivalences introduced by Boltje and Xu ( 2006) to source algebras of p-blocks of finite groups. We show that a p-permutation equivalence between two source algebras A, B of blocks with a common defect group and same local structure induces an isotypy.

Original language | English |
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Pages (from-to) | 1279-1316 |

Number of pages | 38 |

Journal | Transactions of the American Mathematical Society |

Volume | 361 |

Issue number | 3 |

Early online date | 10 Oct 2008 |

Publication status | Published - Mar 2009 |

### Keywords

- source algebras
- fusion systems
- construction
- categories
- characters
- modules

### Cite this

*Transactions of the American Mathematical Society*,

*361*(3), 1279-1316.

**Trivial source bimodule rings for blocks and p-permutation equivalences.** / Linckelmann, Markus.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 361, no. 3, pp. 1279-1316.

}

TY - JOUR

T1 - Trivial source bimodule rings for blocks and p-permutation equivalences

AU - Linckelmann, Markus

PY - 2009/3

Y1 - 2009/3

N2 - We associate with any p-block of a finite group a Grothendieck ring of certain p-permutation bimodules. We extend the notion of p-permutation equivalences introduced by Boltje and Xu ( 2006) to source algebras of p-blocks of finite groups. We show that a p-permutation equivalence between two source algebras A, B of blocks with a common defect group and same local structure induces an isotypy.

AB - We associate with any p-block of a finite group a Grothendieck ring of certain p-permutation bimodules. We extend the notion of p-permutation equivalences introduced by Boltje and Xu ( 2006) to source algebras of p-blocks of finite groups. We show that a p-permutation equivalence between two source algebras A, B of blocks with a common defect group and same local structure induces an isotypy.

KW - source algebras

KW - fusion systems

KW - construction

KW - categories

KW - characters

KW - modules

M3 - Article

VL - 361

SP - 1279

EP - 1316

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -