## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 11, Number 1 (2009), 203-218.

### On $H*(C; k×)$ for fusion systems

#### Abstract

We give a cohomological criterion for the existence and uniqueness of solutions of the $2$-cocycle gluing problem in block theory. The existence of a solution for the $2$-cocycle gluing problem is further reduced to a property of fusion systems of certain finite groups associated with the fusion system of a block.

#### Article information

**Source**

Homology Homotopy Appl., Volume 11, Number 1 (2009), 203-218.

**Dates**

First available in Project Euclid: 1 September 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1251832566

**Mathematical Reviews number (MathSciNet)**

MR2506133

**Zentralblatt MATH identifier**

1245.20066

**Subjects**

Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 18G40: Spectral sequences, hypercohomology [See also 55Txx] 20C20: Modular representations and characters

**Keywords**

Fusion system block 2-cocycle

#### Citation

Linckelmann, Markus. On $H*(C; k×)$ for fusion systems. Homology Homotopy Appl. 11 (2009), no. 1, 203--218. https://projecteuclid.org/euclid.hha/1251832566