Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras
( Memoirs of the American Mathematical Society )
Publication series ：Memoirs of the American Mathematical Society
Author： K. R. Goodearl;M. T. Yakimov
Publisher： American Mathematical Society
Publication year： 2017
E-ISBN: 9781470436940
P-ISBN(Paperback): 9781470436995
Subject： O152.5 Lie group
Keyword： 暂无分类
Language： ENG
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Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras
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
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