In this talk we introduce a signed variant of (valued) quivers and a mutation rule, that generalizes the classical Fomin-Zelevinsky mutation of quivers. We associate to any signed valued quiver a Lie-theoretic object that is a signed analogue of the Cartan counterpart, from which we can construct root systems and a Lie algebra via a "Serre-like" presentation.

We then restrict our attention to the Dynkin case. For root systems, we show some compatibility results with the appropriate concept of mutation. Using results from Barot-Rivera and Perez-Rivera, we also show that signed quivers in the same mutation class yield isomorphic Lie algebras.

This is based on a joint project with Joe Grant (arXiv number 2403.14595).