paper

Relation between generalized and ordinary cluster algebras

arXiv:2512.21062

Abstract

Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their idea and method, we show that the same property holds for any generalized cluster algebra with -variables in an arbitrary semifield. We also present the relations between the -matrices, the -matrices, and the -polynomials of a generalized cluster pattern and those of the corresponding composite cluster pattern.

20 pages ver2: The claim on the Laurent positivity was removed

Relation between generalized and ordinary cluster algebras · wovepaper