Algebras of functions on quantum groups. Part I / Leonid I. Korogodski, Yan S. Soibelman.

Korogodski, Leonid I., author.
Providence, Rhode Island : American Mathematical Society, [1998]
Mathematical surveys and monographs ; volume 56.
Mathematical surveys and monographs, 0076-5376 ; volume 56
1 online resource (162 p.)
Quantum groups.
Function algebras.
Electronic books.
""Contents""; ""Chapter 0. Introduction""; ""Chapter 1. Poisson Lie Groups""; ""1. Poisson manifolds""; ""1.1. Poisson algebras and Poisson manifolds""; ""1.2. Symplectic leaves in a Poisson manifold""; ""2. Lie bialgebras and Manin triples""; ""2.1. Lie bialgebras""; ""2.2. Co-Poisson Hopf algebras""; ""2.3. Manin triples""; ""3. Poisson groups""; ""3.1. Poisson affine algebraic groups and Poisson Hopf algebras""; ""3.2. Poisson Lie groups""; ""3.3. The correspondence between Poisson Lie groups and Lie bialgebras""; ""3.4. Symplectic leaves in Poisson Lie groups and dressing action""
""4. Lie bialgebras and classical r-matrices""""4.1. Coboundary, quasi-triangular and triangular Lie bialgebras""; ""4.2. The classification of quasi-triangular Lie bialgebras""; ""4.3. Frobenius Lie algebras and CYBE""; ""5. Compact Poisson Lie groups""; ""5.1. Quasi-triangular compact Poisson Lie groups""; ""5.2. Symplectic leaves and Bruhat decomposition""; ""5.3. Symplectic leaves in simple complex Poisson Lie groups""; ""6. Poisson G-manifolds""; ""6.1. Poisson G-manifolds and moment maps""; ""6.2. Poisson homogeneous G-manifolds""; ""7. Historical remarks""
""Chapter 2. Quantized Universal Enveloping Algebras""""1. Quantization of Lie bialgebras""; ""1.1. Definition of quantization""; ""1.2. The quantization of complex simple Lie algebras""; ""1.3. Existence and uniqueness of quantization""; ""2. QUE-algebras and R-matrices""; ""2.1. Types of Hopf algebras""; ""2.2. Double Hopf algebras""; ""2.3. The quantum double and the universal quantum R-matrix""; ""2.4. Twisted version of U[sub(h)]g""; ""3. Center of quasi-triangular Hopf algebras""; ""3.1. Two central element constructions""
""3.2. Square of the antipode in the almost-cocommutative case""""3.3. The quasi-triangular case""; ""4. Center of U[sub(h)g and quantum Harish-Chandra homomorphism""; ""4.1. Central elements of U[sub(h)]g""; ""4.2. Quantum Harish-Chandra homomorphism""; ""5. Finite-dimensional U[sub(h)]g-modules""; ""5.1. Finite-dimensional modules and highest weights""; ""5.2. Central characters and the quantum Harish-Chandra homomorphism""; ""6. Tensor products of U[sub(h)]g-modules and tensor categories""; ""7. Fixed quantization parameter""; ""7.1. The complex Hopf algebra U[sub(q)]g""
""7.2. Quasi-R-matrix""""7.3. Admissible finite-dimensional U[sub(q)]g-modules""; ""7.4. Twisted version of U[sub(q)]g""; ""8. Historical remarks""; ""Chapter 3. Quantized Algebras of Functions""; ""1. Main definitions""; ""1.1. Hopf *-algebras""; ""1.2. Quantized algebra of regular functions""; ""2. Properties of the quantized algebras of functions""; ""2.1. Basic properties""; ""2.2. Triangular decomposition of C[G][sub(q)]""; ""2.3. The involution * in C[K][sub(q)]""; ""3. Examples: C[SL[sub(2)](C)][sub(q)] and C[SU(2)][sub(q)]""; ""4. Representation theory of C[SU(2)][sub(q)]""
""4.1. Unitarizable simple C[SL[sub(2)](C)][sub(q)]-modules""
Description based upon print version of record.
Includes bibliographical references.
Description based on online resource; title from PDF title page (ebrary, viewed May 23, 2014).
Soibelman, Yan S., author.
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