05798nam 2200697 a 450 991077906700332120230802004645.0981-4340-45-6(CKB)2550000000087620(EBL)846110(OCoLC)858227992(SSID)ssj0000647338(PQKBManifestationID)11434968(PQKBTitleCode)TC0000647338(PQKBWorkID)10593437(PQKB)11247876(MiAaPQ)EBC846110(WSP)00008081(Au-PeEL)EBL846110(CaPaEBR)ebr10529380(CaONFJC)MIL498441(EXLCZ)99255000000008762020120229d2012 uy 0engur|n|---|||||txtccrQuantized algebra and physics[electronic resource] proceedings of the International Workshop on Quantized Algebra and Physics, Tianjin, China, 23-26 July 2009 /edited by Mo-Lin Ge, Chengming Bai, Naihuan JingHackensack, N.J. World Scientific20121 online resource (215 p.)Nankai series in pure, applied mathematics and theoretical physics ;v. 8Description based upon print version of record.981-4340-44-8 Includes bibliographical references.Preface; CONTENTS; 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-operators2.2.1. O-operators2.2.2. 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 bialgebras5. O-operators and dendriform algebras5.1. 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; ReferencesIrreducible Wakimoto-like Modules for the Affine Lie Algebra gln Yun Gao and Ziting Zeng1. 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. Sergeeva1. Introduction2. 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; ReferencesQuantum Entanglement and Approximation by Positive Matrices Xiaofen Huang and Naihuan JingThe book aims to survey recent developments in quantum algebras and related topics. Quantum groups were introduced by Drinfeld and Jimbo in 1985 in their work on Yang-Baxter equations. The subject from the very beginning has been an interesting one for both mathematics and theoretical physics. For example, Yangian is a special example of quantum group, corresponding to rational solution of Yang-Baxter equation. Viewed as a generalization of the symmetric group, Yangians also have close connections to algebraic combinatorics. This is the proceeding for the International Workshop on Quantized AlNankai series in pure, applied mathematics and theoretical physics ;v. 8.Quantum groupsCongressesPhysicsCongressesQuantum theoryCongressesQuantum groupsPhysicsQuantum theory530.143Bai Chengming1546468Ge M. L(Mo-Lin)52157Jing Naihuan66711International Workshop on Quantized Algebra and PhysicsMiAaPQMiAaPQMiAaPQBOOK9910779067003321Quantized algebra and physics3810900UNINA