| eBook ISBN: | 978-1-4704-3639-1 |
| Product Code: | MEMO/246/1165.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
| eBook ISBN: | 978-1-4704-3639-1 |
| Product Code: | MEMO/246/1165.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 246; 2016; 94 ppMSC: Primary 53; 13
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.
-
Table of Contents
-
Chapters
-
1. Introduction
-
2. Cluster structures and Poisson–Lie groups
-
3. Main result and the outline of the proof
-
4. Initial cluster
-
5. Initial quiver
-
6. Regularity
-
7. Quiver transformations
-
8. Technical results on cluster algebras
-
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
-
Chapters
-
1. Introduction
-
2. Cluster structures and Poisson–Lie groups
-
3. Main result and the outline of the proof
-
4. Initial cluster
-
5. Initial quiver
-
6. Regularity
-
7. Quiver transformations
-
8. Technical results on cluster algebras
