Exotic cluster structures on SLn : the Cremmer-Gervais case
著者
書誌事項
Exotic cluster structures on SLn : the Cremmer-Gervais case
（Memoirs of the American Mathematical Society, no. 1165）
American Mathematical Society, c2016
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注記
"Volume 246, number 1165 (fourth of 6 numbers), March 2017"
Includes bibliographical references (p. 93-94)
内容説明・目次
内容説明
This is the second paper in the series of papers dedicated to the study of natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on $\mathcal{G}$ corresponds to a cluster structure in $\mathcal{O}(\mathcal{G})$. The authors have shown before that this conjecture holds for any $\mathcal{G}$ in the case of the standard Poisson-Lie structure and for all Belavin-Drinfeld classes in $SL_n$, $n<5$. In this paper the authors establish it for the Cremmer-Gervais Poisson-Lie structure on $SL_n$, which is the least similar to the standard one.
目次
Introduction
Cluster structures and Poisson-Lie groups
Main result and the outline of the proof
Initial cluster
Initial quiver
Regularity
Quiver transformations
Technical results on cluster algebras
Bibliography
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