1 research outputs found
Decomposition theory of modules: the case of Kronecker algebra
Let be a finite-dimensional algebra over an algebraically closed field
. For any finite-dimensional -module we give a general formula
that computes the indecomposable decomposition of 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 Mr\'oz. As an example we apply this formula to the
Kronecker algebra and give an explicit formula to compute the
indecomposable decomposition of , which enables us to make a computer
program