10% off all books and free delivery over £40
Buy from our bookstore and 25% of the cover price will be given to a school of your choice to buy more books. *15% of eBooks.

Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras

View All Editions (1)

The selected edition of this book is not available to buy right now.
Add To Wishlist
Write A Review

About

Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras Synopsis

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.

About This Edition

ISBN: 9781470436940
Publication date:
Author: K R Goodearl, Milen Yakimov
Publisher: American Mathematical Society
Format: Paperback
Pagination: 119 pages
Series: Memoirs of the American Mathematical Society
Genres: Algebraic geometry
Algebra