Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras
Apr 2017 · Memoirs of the American Mathematical Society Book 250 · American Mathematical Soc.
Ebook
119
Pages
About this ebook
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
About the author
K. R. Goodearl: University of California, Santa Barbara,
M. T. Yakimov: Louisiana State University, Baton Rouge
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