Rigids as iterated skew commutators of simples.
Let \(k\) be a finite field, and \(A\) be a finite-dimensional hereditary \(k\)-algebra which is not of wild representation type. Let further \(\mathcal H(A)\) denote the Ringel-Hall algebra of \(A\), and \(\mathcal C(A)\) denote the subalgebra of \(\mathcal H(A)\), generated by the isoclasses of simple \(A\)-modules. The main result of this paper asserts that for any \(A\)-module \(M\) such that \(\text{Ext}^1_A(M,M)=0\) (such modules \(M\) are sometimes called rigid) the class \([M]\) of \(M\) in \(\mathcal C(A)\) can be written as an iterated skew commutator of the isoclasses of simple \(A\)-modules. This, in particular, gives a new characterization of rigidness for indecomposable modules over a tame hereditary algebra.
scientific article; zbMATH DE number 5080841