Cluster structures with non-integer quivers

点击翻译按钮获取中文摘要

Cluster algebras were introduced and studied by Fomin and Zelevinsky in 2000, since then the structure appeared in numerous different fields of mathematics and theoretical physics. The structure is induced by a quiver, i.e. a finite oriented graph with integer weights of arrows. Recently, an analogue of the structure was proposed for quivers with real weights of arrows. The aim of the current work will be to develop a number of geometric, combinatorial, algebraic and representation theoretic interpretations of this new structure and to obtain its applications.