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QUANTISATION SPACES OF CLUSTER ALGEBRAS

Part of: Arithmetic rings and other special rings

Published online by Cambridge University Press:  04 September 2017

FLORIAN GELLERT  and
PHILIPP LAMPE
FLORIAN GELLERT
Affiliation:
Faculty of Mathematics, Bielefeld University, PO Box 100 131, 33501 Bielefeld, Germany e-mails: florian.gellert@math.uni-bielefeld.de, lampe@math.uni-bielefeld.de
PHILIPP LAMPE
Affiliation:
Faculty of Mathematics, Bielefeld University, PO Box 100 131, 33501 Bielefeld, Germany e-mails: florian.gellert@math.uni-bielefeld.de, lampe@math.uni-bielefeld.de
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Abstract

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The article concerns the existence and uniqueness of quantisations of cluster algebras. We prove that cluster algebras with an initial exchange matrix of full rank admit a quantisation in the sense of Berenstein-Zelevinsky and give an explicit generating set to construct all quantisations.

MSC classification

Primary: 13F60: Cluster algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 2 , May 2018 , pp. 273 - 284
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

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