Euler characteristics of quiver Grassmannians and Ringel-Hall algebras of string algebras.
The author computes the Euler characteristics of quiver Grassmannians and quiver flag varieties of tree and band modules and proves their positivity. As an application, the author considers the Ringel-Hall algebra \(\mathcal C(A)\) of a string algebra \(A\) and computes, in combinatorial terms, the product of arbitrary functions in \(\mathcal C(A)\). Finally, it is shown that the Euler characteristics of a quiver Grassmannian for some finite dimensional representation of a locally finite quiver is determined by the Euler characteristics of the quiver Grassmannian for a free covering of the corresponding quiver and module.
scientific article; zbMATH DE number 6119049
scientific article