Finitistic dimensions and piecewise hereditary property of skew group algebras

Liping Li

K-Theory and Homology Representation Theory Rings and Algebras mathscidoc: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.
No keywords uploaded!
[ Download ] [ 2017-02-22 10:41:03 uploaded by LipingLi ] [ 77 downloads ] [ 0 comments ]
@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.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved