Applications of the freezing operators on cluster algebras
Fan Qin
TL;DR
This paper explores how freezing operators can relate various quantum cluster algebras, preserving bases and monomials, and establishing connections between different algebraic constructions.
Contribution
It demonstrates that freezing operators map cluster monomials to monomials and bases to bases, linking different quantum upper cluster algebras and their basis constructions.
Findings
Freezing operators preserve localized quantum cluster monomials.
They map bases to bases in many cases.
Bases via freezing coincide with those via localization.
Abstract
We apply freezing operators to relate different (quantum) upper cluster algebras. We prove that these operators send localized (quantum) cluster monomials to localized (quantum) cluster monomials. They also send bases to bases in many cases. In addition, the bases constructed via freezing coincide with those constructed via localization.
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