Exotic Cluster Structures on $SL_n$: the Cremmer-Gervais Case

M. Gekhtman, M. Shapiro, A. Vainshtein (Autoren)

Buch | Softcover

94 Seiten

2017
American Mathematical Society (Verlag)
978-1-4704-2258-5 (ISBN)

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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.

M. Gekhtman, University of Notre Dame, IN. M. Shapiro, Michigan State University, East Lansing, MI. A. Vainshtein, University of Haifa, Israel.

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

Erscheinungsdatum	01.02.2017
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	201 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-2258-1 / 1470422581
ISBN-13	978-1-4704-2258-5 / 9781470422585
Zustand	Neuware