Free Delivery Over $100
|
|
|||
|
||||
OverviewAll 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. Full Product DetailsAuthor: K.R. Goodearl , M.T. YakimovPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.200kg ISBN: 9781470436940ISBN 10: 1470436949 Pages: 119 Publication Date: 30 May 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 Quantum cluster algebras Iterated skew polynomial algebras and noncommutative UFDs One-step mutations in CGL extensions Homogeneous prime elements for subalgebras of symmetric CGL extensions Chains of mutations in symmetric CGL extensions Division properties of mutations between CGL extension presentations Symmetric CGL extensions and quantum cluster algebras Quantum groups and quantum Schubert cell algebras Quantum cluster algebra structures on quantum Schubert cell algebras Bibliography IndexReviewsAuthor InformationK. R. Goodearl, University of California, Santa Barbara. M. T. Yakimov, Louisiana State University, Baton Rouge. Tab Content 6Author Website:Countries AvailableAll regions |
||||
