A note on species realizations and nondegeneracy of potentials

Abstract

In this note we show that a mutation theory of species with potential can be defined so that a certain class of skew-symmetrizable integer matrices have a species realization admitting a non-degenerate potential. This gives a partial affirmative answer to a question raised by Jan Geuenich and Daniel Labardini-Fragoso. We also provide an example of a class of skew-symmetrizable $4 \times 4$ integer matrices, which are not globally unfoldable nor strongly primitive, and that have a species realization admitting a non-degenerate potential.