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OverviewThis 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. Full Product DetailsAuthor: M. Gekhtman , M. Shapiro , A. VainshteinPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.201kg ISBN: 9781470422585ISBN 10: 1470422581 Pages: 94 Publication Date: 30 March 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction 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 BibliographyReviewsAuthor InformationM. Gekhtman, University of Notre Dame, IN. M. Shapiro, Michigan State University, East Lansing, MI. A. Vainshtein, University of Haifa, Israel. Tab Content 6Author Website:Countries AvailableAll regions |
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