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Titlebook: Quantum Groups in Three-Dimensional Integrability; Atsuo Kuniba Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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發(fā)表于 2025-3-21 17:24:18 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Quantum Groups in Three-Dimensional Integrability
編輯Atsuo Kuniba
視頻videohttp://file.papertrans.cn/782/781225/781225.mp4
概述Presents quantized coordinate ring as a main player dual to what is usually meant by quantum group in physics literature.Illustrates quantization of the conventional Yang–Baxter and reflection equatio
叢書名稱Theoretical and Mathematical Physics
圖書封面Titlebook: Quantum Groups in Three-Dimensional Integrability;  Atsuo Kuniba Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive
描述Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by?.U.q.?and?.A.q.. The former is a deformation of the universal enveloping algebra of a Kac–Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on?.U.q., and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions..?.This book aims to present a unique approach to 3-dimensional integrability based on?.A.q.. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang–Baxter equation, and its solution due to work by Kapranov–Voevodsky (1994)..?.Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincaré–Birkhoff–Witt basis of a unipotent part of?.U.q., reductions to the solutions of the Yang–Baxter equation, reflection equation,?.G.2.?reflectio
出版日期Book 2022
關(guān)鍵詞Quantized Coordinate Ring; Tetrahedron /3D Reflection Equations; PBW Basis of Positive Part of Quantiz
版次1
doihttps://doi.org/10.1007/978-981-19-3262-5
isbn_softcover978-981-19-3264-9
isbn_ebook978-981-19-3262-5Series ISSN 1864-5879 Series E-ISSN 1864-5887
issn_series 1864-5879
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor
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沙發(fā)
發(fā)表于 2025-3-21 21:45:01 | 只看該作者
3D Reflection Equation and Quantized Reflection Equation,This chapter is a brief introduction to the 3D reflection equation and the quantized reflection equation. They are both fundamental and will work coherently in later chapters of the book. In addition to the 3D . satisfying the tetrahedron equation, a central role is played by a linear operator which we call 3D ..
板凳
發(fā)表于 2025-3-22 03:58:18 | 只看該作者
地板
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發(fā)表于 2025-3-22 12:45:47 | 只看該作者
978-981-19-3264-9The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor
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發(fā)表于 2025-3-22 15:17:59 | 只看該作者
Quantum Groups in Three-Dimensional Integrability978-981-19-3262-5Series ISSN 1864-5879 Series E-ISSN 1864-5887
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發(fā)表于 2025-3-22 18:41:10 | 只看該作者
Theoretical and Mathematical Physicshttp://image.papertrans.cn/q/image/781225.jpg
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發(fā)表于 2025-3-23 02:43:42 | 只看該作者
3D , From Quantized Coordinate Ring of Type C,tructed explicitly. They lead to solutions of the 3D reflection equation and the quantized reflection equation. The 3D . admits the set-theoretical and birational counterparts. These features are parallel with Chap. . for type A.
10#
發(fā)表于 2025-3-23 08:57:27 | 只看該作者
3D , From Quantized Coordinate Ring of Type A,to a . deformation of the algebra of functions on the Lie group of .. It will be called the quantized coordinate ring and denoted by . in this book. We assume that . is generic throughout. In this chapter, . for . of type A is treated based on a concrete realization by generators and relations, defe
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