2017/03/23 by Asashiba, Hideto, Nakashima, Ken, Yoshiwaki, Michio
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1703.07906
Let A be a finite-dimensional algebra over an algebraically closed field \Bbbk. For any finite-dimensional A-module M we give a general formula that computes the indecomposable decomposition of M without decomposing it, for which we use the knowledge of AR-quivers that are already computed in many cases. The proof of the formula here is much simpler than that in a prior literature by Dowbor and Mróz. As an example we apply this formula to the Kronecker algebra A and give an explicit formula to compute the indecomposable decomposition of M, which enables us to make a computer program.