2018/01/18 by Pastuszak, Grzegorz · 1 citation
#16G20 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1801.05979
Assume that K is an algebraically closed field, R a locally support-finite locally bounded K-category, G a torsion-free admissible group of K-linear automorphisms of R and A=R/G. We show that the Krull-Gabriel dimension KG(R) of R is finite if and only if the Krull-Gabriel dimension KG(A) of A is finite. In these cases KG(R)=KG(A). We apply this result to determine the Krull-Gabriel dimension of standard selfinjective algebras of polynomial growth. Finally, we show that there are no super-decomposable pure-injective modules over standard selfinjective algebras of domestic type.