# MathSciDoc: An Archive for Mathematician ∫

#### K-Theory and HomologyRepresentation TheoryRings and Algebrasmathscidoc:1702.20001

Glasgow Math. J., 57, 509-517, 2015
Let \$\Lambda\$ be a finite dimensional algebra and \$G\$ be a finite group whose elements act on \$\Lambda\$ as algebra automorphisms. Under the assumption that \$\Lambda\$ has a complete set \$E\$ of primitive orthogonal idempotents, closed under the action of a Sylow \$p\$-subgroup \$S \leqslant G\$, we show that the skew group algebra \$\Lambda G\$ and \$\Lambda\$ have the same finitistic dimension and the same strong global dimension if the action of \$S\$ on \$E\$ is free. Using a homological characterization of piecewise hereditary algebras proved by Happel and Zacharia, we deduce that \$\Lambda G\$ is piecewise hereditary if and only if \$S\$ acts freely on \$E\$ and \$\Lambda\$ is piecewise hereditary as well.
```@inproceedings{liping2015finitistic,
title={Finitistic dimensions and piecewise hereditary property of skew group algebras},
author={Liping Li},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222104103926346493},
booktitle={Glasgow Math. J.},
volume={57},
pages={509-517},
year={2015},
}
```
Liping Li. Finitistic dimensions and piecewise hereditary property of skew group algebras. 2015. Vol. 57. In Glasgow Math. J.. pp.509-517. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222104103926346493.