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Quantum Cluster Algebras Structures on Quantum Nilpotent Algebras.


Quantum Cluster Algebras Structures on Quantum Nilpotent Algebras

K. R. Goodearl and M. T. Yakimov

American Mathematical Society


119 pages


Memoirs of the American Mathematical Society; Volume 247, Number 1169


Goodearl and Yakimov prove that all algebras in a very large, axiomatically defined class of quantum nilpotent algebras possess quantum cluster algebra structures under mild conditions. Furthermore, they show that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for constructing (quantum) cluster algebra structures on (quantum) coordinate rings arising in Lie theory were done on a case-by-case basis, relying on the combinatorics of each concrete family, they say, and these findings will make that unnecessary. ([umlaut] Ringgold, Inc., Portland, OR)

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Date:May 1, 2017
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