### Abstract

The block variety V-G.b(M) of a finitely generated indecomposable module M over the block algebra of a p-block b of a finite group G, introduced in (J. Algebra 215 (1999) 460), can be computed in terms of a vertex and a source of M. We use this to show that VG,b(M) is connected, and that every closed homogeneous subvariety of the affine variety VG.b defined by block cohomology H*(G, b) (cf. Al.-ebras Rep. Theory 2 (1999) 107) is the variety of a module over the block algebra. This is analogous to the corresponding statements on Carlson's cohomology varieties in (lnvent. Math. 77 (1984) 291). © 2004 Elsevier B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 11-17 |

Number of pages | 7 |

Journal | Journal of Pure and Applied Algebra |

Volume | 197 |

Issue number | 1-3 |

Early online date | 21 Nov 2004 |

DOIs | |

Publication status | Published - 1 May 2005 |

### Keywords

- source algebras

### Cite this

*Journal of Pure and Applied Algebra*,

*197*(1-3), 11-17. https://doi.org/10.1016/j.jpaa.2004.08.032

**Vertex and source determine the block variety of an indecomposable module.** / Benson, David John; Linckelmann, Markus.

Research output: Contribution to journal › Article

*Journal of Pure and Applied Algebra*, vol. 197, no. 1-3, pp. 11-17. https://doi.org/10.1016/j.jpaa.2004.08.032

}

TY - JOUR

T1 - Vertex and source determine the block variety of an indecomposable module

AU - Benson, David John

AU - Linckelmann, Markus

PY - 2005/5/1

Y1 - 2005/5/1

N2 - The block variety V-G.b(M) of a finitely generated indecomposable module M over the block algebra of a p-block b of a finite group G, introduced in (J. Algebra 215 (1999) 460), can be computed in terms of a vertex and a source of M. We use this to show that VG,b(M) is connected, and that every closed homogeneous subvariety of the affine variety VG.b defined by block cohomology H*(G, b) (cf. Al.-ebras Rep. Theory 2 (1999) 107) is the variety of a module over the block algebra. This is analogous to the corresponding statements on Carlson's cohomology varieties in (lnvent. Math. 77 (1984) 291). © 2004 Elsevier B.V. All rights reserved.

AB - The block variety V-G.b(M) of a finitely generated indecomposable module M over the block algebra of a p-block b of a finite group G, introduced in (J. Algebra 215 (1999) 460), can be computed in terms of a vertex and a source of M. We use this to show that VG,b(M) is connected, and that every closed homogeneous subvariety of the affine variety VG.b defined by block cohomology H*(G, b) (cf. Al.-ebras Rep. Theory 2 (1999) 107) is the variety of a module over the block algebra. This is analogous to the corresponding statements on Carlson's cohomology varieties in (lnvent. Math. 77 (1984) 291). © 2004 Elsevier B.V. All rights reserved.

KW - source algebras

U2 - 10.1016/j.jpaa.2004.08.032

DO - 10.1016/j.jpaa.2004.08.032

M3 - Article

VL - 197

SP - 11

EP - 17

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1-3

ER -