Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras

Ebook Details


K. R. Goodearl, M. T. Yakimov

Year 2017
Pages 119
Publisher Amer Mathematical Society
Language en
ISBN 9781470436940
File Size 962.32 KB
File Format PDF
Download Counter 109
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Ebook Description

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.