Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras. (Record no. 128033)
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| fixed length control field | 03481nam a22004693i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4908291 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131329.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2017 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470436995 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470436940 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4908291 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4908291 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11409836 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)982296190 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA251.3.G663 2017 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.54999999999995 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Goodearl, K. R. |
| 245 10 - TITLE STATEMENT | |
| Title | Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2017. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (134 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.247 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Quantum cluster algebras -- Chapter 3. Iterated skew polynomial algebras and noncommutative UFDs -- Chapter 4. One-step mutations in CGL extensions -- Chapter 5. Homogeneous prime elements for subalgebras of symmetric CGL extensions -- Chapter 6. Chains of mutations in symmetric CGL extensions -- Chapter 7. Division properties of mutations between CGL extension presentations -- Chapter 8. Symmetric CGL extensions and quantum cluster algebras -- Chapter 9. Quantum groups and quantum Schubert cell algebras -- Chapter 10. Quantum cluster algebra structures on quantum Schubert cell algebras -- Bibliography -- Index -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Quantum groups. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Yakimov, M. T. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Goodearl, K. R. |
| Title | Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2017 |
| International Standard Book Number | 9781470436940 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908291">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908291</a> |
| Public note | Click to View |
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