Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Exotic cluster structures on SLn : the Cremmer-Gervais case / M. Gekhtman, M. Shapiro and A. Vainshtein.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 246, no 1165.Publication details: Providence : American Mathematical Society, 2017.Description: v, 94 pages : illustrations ; 26 cmISBN:
  • 9781470422585 (pbk : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
Chapter 1. Introduction -- Chapter 2. Cluster structures and Poisson-Lie groups -- Chapter 3. Main result and the outline of the proof -- Chapter 4. Initial cluster -- Chapter 5. Initial quiver -- Chapter 6. Regularity -- Chapter 7. Quiver transformations -- Chapter 8. Technical results on cluster algebras.
Summary: 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 G corresponds to a cluster structure in O(G). We have shown before that this conjecture holds for any G in the case of the standard Poisson–Lie structure and for all Belavin-Drinfeld classes in SLn, n < 5. In this paper we establish it for the Cremmer–Gervais Poisson–Lie structure on SLn, which is the least similar to the standard one.
Tags from this library: No tags from this library for this title. Log in to add tags.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 138207
Total holds: 0

Includes bibliographical references.

Chapter 1. Introduction --
Chapter 2. Cluster structures and Poisson-Lie groups --
Chapter 3. Main result and the outline of the proof --
Chapter 4. Initial cluster --
Chapter 5. Initial quiver --
Chapter 6. Regularity --
Chapter 7. Quiver transformations --
Chapter 8. Technical results on cluster algebras.

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 G corresponds to a cluster structure in O(G). We have shown before that this conjecture holds for any G in the case of the standard Poisson–Lie structure and for all Belavin-Drinfeld classes in SLn, n < 5. In this paper we establish it for the Cremmer–Gervais Poisson–Lie structure on SLn, which is the least similar to the standard one.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in