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作者 Bai, Chengming
書名 Quantized Algebra and Physics - Proceedings of the International Workshop : Proceeding of the International Workshop
出版項 Singapore : World Scientific Publishing Co Pte Ltd, 2011
©2012
國際標準書號 9789814340458 (electronic bk.)
9789814340441
book jacket
說明 1 online resource (215 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Series In Mathematical Biology And Medicine ; v.8
Series In Mathematical Biology And Medicine
附註 Intro -- CONTENTS -- Preface -- Programs -- A Note on Brauer-Schur Functions Kazuya Aokage, Hiroshi Mizukawa and Hiro-Fumi Yamada -- 1. Introduction -- 2. Brauer-Schur functions -- 3. Cauchy type formula -- 4. Monomial expansion -- References -- O-Operators on Associative Algebras, Associative Yang-Baxter Equations and Dendriform Algebras Chengming Bai, Li Guo and Xiang Ni -- 1. Introduction -- 1.1. Rota-Baxter algebras, Yang-Baxter equations and dendriform algebras -- 1.2. O-operators and layout of the paper -- 2. O-operators and extended O-operators -- 2.1. Bimodules and A-bimodule k-algebras -- 2.2. Extended O-operators -- 2.2.1. O-operators -- 2.2.2. Balanced homomorphisms -- 2.2.3. Extended O-operators -- 2.3. Extended O-operators, O-operators and Rota-Baxter operators: the first connection -- 3. Extended O-operators and AYBE -- 3.1. Extended AYBE -- 3.2. From EAYBE to Extended O-operators -- 3.3. From extended O-operators to EAYBE -- 3.3.1. The general case -- 3.3.2. The case of Frobenius algebras -- 4. Antisymmetric infinitesimal bialgebras and generalized AYBE -- 4.1. Antisymmetric infinitesimal bialgebras, generalized AYBE and extended O-operators -- 4.2. Factorizable quasitriangular antisymmetric infinitesimal bialgebras -- 5. O-operators and dendriform algebras -- 5.1. Rota-Baxter algebras and dendriform algebras -- 5.2. From O-operators to dendriform algebras on the domains -- 5.3. From O-operators to dendriform algebras on the ranges -- 6. O-operators, Rota-Baxter operators, relative differential operators, dendriform algebras and AYBEs -- 6.1. O-operators and Rota-Baxter operators: the second connection -- 6.2. Relative differential operators and Rota-Baxter operators -- 6.3. Characterizations of dendriform algebras in terms of bimodules and associativity -- 6.4. Dendriform algebras and AYBEs -- Acknowledgements -- References
Irreducible Wakimoto-like Modules for the Affine Lie Algebra gln Yun Gao and Ziting Zeng -- 1. Introduction -- 2. Finite dimensional case -- 3. Affine case -- References -- Verma Modules over Generic Exp-Polynomial Lie Algebras Xiangqian Guo, Xuewen Liu and Kaiming Zhao -- 1. Introduction -- 2. Main results and applications -- 3. Properties on generic exp-polynomial functions -- 4. Verma modules over generic exp-polynomial Lie algebras -- Acknowledgments -- References -- A Formal Infinite Dimensional Cauchy Problem and its Relation to Integrable Hierarchies G. F. Helminck, E. A. Panasenko and A. O. Sergeeva -- 1. Introduction -- 2. The finite dimensional setting -- 3. The Cauchy problem: infinite dimensional case -- 4. The Cauchy problem in integrable hierarchies -- 4.1. Lower triangular matrices -- 4.2. The Lax equations of the ( k, h 0)-hierarchy -- 4.3. The zero curvature form of the hierarchy -- 4.4. Wave matrices for the ( k, h 0)-hierarchy -- 4.5. The relation with Cauchy problems -- References -- Partially Harmonic Tensors and Quantized Schur-Weyl Duality Jun Hu and Zhankui Xiao -- 1. Introduction -- 2. Quantized Enveloping Algebra and BMW Algebra -- Acknowledgments -- References -- Quantum Entanglement and Approximation by Positive Matrices Xiaofen Huang and Naihuan Jing -- 1. Introduction -- 2. Approximation by Positive Definite Matrices -- 3. Sums of Matrices and Estimates -- 4. Lie Algebras and Approximation of Summations -- 5. Conclusion -- Acknowledgments -- References -- 2-Partitions of Root Systems Bin Li, William Wong and Hechun Zhang -- 1. Introduction -- 2. Preliminaries -- 3. 2-partitions of the root system of finite type -- 4. 2-partitions of the root system of finite type -- 5. 2-partitions of the root system of affine type -- Acknowledgments -- References -- A Survey on Weak Hopf Algebras Fang Li and Qinxiu Sun
Introduction and Algebraic Structures -- 1. Generalized quantum double and singular solutions of QYBE -- 2. Constructing quantum enveloping algebras via weak Hopf structures -- 3. Generalizations of tensor category from weak Hopf algebras -- Acknowledgments -- References -- The Equitable Presentation for the Quantum Algebra Uq(f(k)) Yan Pan, Meiling Zhu and Libin Li -- Introduction -- 1. The Algebra Uq( f (k)) -- 2. The Equitable Presentation for Uq( f (k)) -- 3. The Elements y and z Are Not Invertible in Uq( f (k)) -- 4. The Elements y and z Are Invertible on Each Finite Dimensional Uq( f (k))-Module -- 5. The Elements nx, ny, nz -- 6. Some Formulae Involving the q-Exponential Function -- 7. The Operator -- Acknowledgments -- References
Key Features:The book emphasizes recent developments in the algebraic aspect of the theory. Contributors include mathematicians from USA, China, Australia, Canada, Europe and Japan
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Bai, Chengming Quantized Algebra and Physics - Proceedings of the International Workshop : Proceeding of the International Workshop Singapore : World Scientific Publishing Co Pte Ltd,c2011 9789814340441
主題 Quantum groups -- Congresses.;Physics -- Congresses.;Quantum theory -- Congresses
Electronic books
Alt Author Ge, Mo-lin
Jing, Naihuan
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