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A=U for Locally Acyclic Cluster Algebras

Greg Muller

Symmetry Integrability and Geometry Methods and Applications · 2014 · 36 citations · 10 references

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Concepts

Abstract

This note presents a self-contained proof that acyclic and locally acyclic cluster algebras coincide with their upper cluster algebras.

References

10

Cluster algebras I: Foundations

Sergey Fomin, Andrei Zelevinsky · Journal of the American Mathematical Society · 2001 · 1.7K citations · Full text

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Cluster algebras and triangulated surfaces. Part I: Cluster complexes

Sergey Fomin, Michael Shapiro, Dylan P. Thurston · Acta Mathematica · 2008 · 605 citations · Full text

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Cluster algebras IV: Coefficients

Sergey Fomin, Andrei Zelevinsky · Compositio Mathematica · 2007 · 603 citations · Full text

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Cluster algebras III: Upper bounds and double Bruhat cells

Arkady Berenstein, Sergey Fomin, Andrei Zelevinsky · Duke Mathematical Journal · 2005 · 581 citations

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Cluster algebras and Weil-Petersson forms

Michael Gekhtman, Michael Shapiro, Alek Vainshtein · Duke Mathematical Journal · 2005 · 157 citations · Full text

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