000			03481nam a22004693i 4500
001			EBC4908291
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005			20240729131329.0
006			m o d |
007			cr cnu||||||||
008			240724s2017 xx o ||||0 eng d
020			_a9781470436995 _q(electronic bk.)
020			_z9781470436940
035			_a(MiAaPQ)EBC4908291
035			_a(Au-PeEL)EBL4908291
035			_a(CaPaEBR)ebr11409836
035			_a(OCoLC)982296190
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA251.3.G663 2017
082	0		_a512.54999999999995
100	1		_aGoodearl, K. R.
245	1	0	_aQuantum Cluster Algebra Structures on Quantum Nilpotent Algebras.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2017.
264		4	_c©2016.
300			_a1 online resource (134 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.247
505	0		_aCover -- 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			_aAll 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			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aQuantum groups.
655		4	_aElectronic books.
700	1		_aYakimov, M. T.
776	0	8	_iPrint version: _aGoodearl, K. R. _tQuantum Cluster Algebra Structures on Quantum Nilpotent Algebras _dProvidence : American Mathematical Society,c2017 _z9781470436940
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908291 _zClick to View
999			_c128033 _d128033