Minimal right determiners of irreducible morphisms in tree string algebras

Let [Formula: see text] be a finite dimensional string algebra over a field with the quiver [Formula: see text] such that the underlying graph of [Formula: see text] is a tree, and let [Formula: see text] be the number of the minimal right determiners of all irreducible morphisms between indecomposable left [Formula: see text]-modules. Then we have [Formula: see text] where [Formula: see text] is the number of vertices in [Formula: see text], [Formula: see text] is a source in [Formula: see text] with two neighbors[Formula: see text] and [Formula: see text] is the number of vertices such that the associated vertex ideals are not zero.

THE ZERO TENSION LIMIT OF THE VIRASORO ALGEBRA AND THE CENTRAL EXTENSION

We argue that the Virasoro algebra for the closed bosonic string can be cast in a form which is suitable for the limit of vanishing string tension. In this form the limit of the Virasoro algebra gives the null string algebra. The anomalous central extension is seen to vanish as well when T→0.