@article{Jia2023, 
author = {Wanwan Jia and Fang Li},
title = {Invariant properties of modules under smash products from finite dimensional algebras},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {6737-6748},
keywords = {finite dimensional algebra, smash product, indecomposable module, G-stable module, stable category, abelian},
url = {https://www.sciopen.com/article/10.3934/math.2023342},
doi = {10.3934/math.2023342},
abstract = {We give the relationship between indecomposable modules over the finite dimensional    k-algebra    A and the smash product    A  ♯  G respectively, where    G is a finite abelian group satisfying    G  ⊆  A  u  t  (  A  ), and    k is an algebraically closed field with the characteristic not dividing the order of    G. More precisely, we construct all indecomposable    A  ♯  G-modules from indecomposable    A-modules and prove that an    A  ♯  G-module is indecomposable if and only if it is an indecomposable    G-stable module over    A. Besides, we give the relationship between simple, projective and injective modules in    m  o  d  A and those in    m  o  d  A  ♯  G.}
}