Mutation of signed valued quivers and presentations of simple complex Lie algebras

Autor:	Grant, Joseph, Morigi, Davide
Rok vydání:	2024
Předmět:	Mathematics - Representation Theory Mathematics - Rings and Algebras Primary: 17B20 Secondary: 17B22 13F60
Druh dokumentu:	Working Paper
Popis:	We introduce a signed variant of (valued) quivers and a mutation rule that generalizes the classical Fomin-Zelevinsky mutation of quivers. To any signed valued quiver we associate a matrix that is a signed analogue of the Cartan counterpart appearing in the theory of cluster algebras. From this matrix, we construct a Lie algebra via a "Serre-like" presentation. In the mutation Dynkin case, we define root systems using the signed Cartan counterpart and show compatibility with mutation of roots as defined by Parsons. Using results from Barot-Rivera and P\'erez-Rivera, we show that mutation equivalent signed quivers yield isomorphic Lie algebras, giving presentations of simple complex Lie algebras. Comment: Small changes, improved abstract
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.14595 Zobrazit plný text záznamu View this record from Arxiv