Lectures on Algebraic Quantum Groups by Ken Brown
In September 2000, at the Centre de Recerca Matematica in Barcelona, we pre sented a 30-hour Advanced Course on Algebraic Quantum Groups. After the course, we expanded and smoothed out the material presented in the lectures and inte grated it with the background material that we had prepared for the participants; this volume is the result. As our title implies, our aim in the course and in this text is to treat selected algebraic aspects of the subject of quantum groups. Sev eral of the words in the previous sentence call for some elaboration. First, we mean to convey several points by the term 'algebraic' - that we are concerned with algebraic objects, the quantized analogues of 'classical' algebraic objects (in contrast, for example, to quantized versions of continuous function algebras on compact groups); that we are interested in algebraic aspects of the structure of these objects and their representations (in contrast, for example, to applications to other areas of mathematics); and that our tools will be drawn primarily from noncommutative algebra, representation theory, and algebraic geometry. Second, the term 'quantum groups' itself. This label is attached to a large and rapidly diversifying field of mathematics and mathematical physics, originally launched by developments around 1980 in theoretical physics and statistical me chanics. It is a field driven much more by examples than by axioms, and so resists attempts at concise description (but see Chapter 1. 1 and the references therein).-
Harmonic and Geometric Analysis
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Integral Geometry and Valuations
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Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension
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Mean Curvature Flow and Isoperimetric Inequalities
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Elliptic Curves, Hilbert Modular Forms and Galois Deformations
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Contemporary Cryptology
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The Geometry of the Word Problem for Finitely Generated Groups
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Simplicial Methods for Operads and Algebraic Geometry
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Combinatorial Number Theory and Additive Group Theory
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Compactifying Moduli Spaces
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Ramsey Methods in Analysis
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Group-based Cryptography
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Hyperbolic Cross Approximation
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Central Configurations, Periodic Orbits, and Hamiltonian Systems
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Crossed Products of C*-Algebras, Topological Dynamics, and Classification
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Numerical Solutions of Partial Differential Equations
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Proper Group Actions and the Baum-Connes Conjecture
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Homotopy Theoretic Methods in Group Cohomology
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An Introduction to Piecewise Smooth Dynamics
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Geometry and Dynamics of Integrable Systems
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Building Bridges Between Algebra and Topology
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Combinatorial Matrix Theory
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Polynomial Identity Rings
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Kolmogorov Equations for Stochastic PDEs
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String Topology and Cyclic Homology
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Symplectic Geometry of Integrable Hamiltonian Systems
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Algorithmic and Geometric Topics Around Free Groups and Automorphisms
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Geometry and Quantization of Moduli Spaces
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From Levy-Type Processes to Parabolic SPDEs
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Variable Lebesgue Spaces and Hyperbolic Systems
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Higher Structures and Operadic Calculus
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Advances in Poisson Geometry
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Analysis on h-Harmonics and Dunkl Transforms
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An Introduction to C*-Algebras and the Classification Program
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Global Riemannian Geometry: Curvature and Topology
"The proofs, sketches of proofs, and quotations from the literature are carefully writtenNumerous examples and exercises are included, and bibliographical notes conclude each chapter. The second and third parts end with a discussion of open problems and perspectives for further research."
--Mathematical Reviews
| SKU | Unavailable |
| ISBN 13 | 9783764367145 |
| ISBN 10 | 3764367148 |
| Title | Lectures on Algebraic Quantum Groups |
| Author | Ken Brown |
| Series | Advanced Courses In Mathematics - Crm Barcelona |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Birkhauser Verlag AG |
| Year published | 2002-04-01 |
| Number of pages | 348 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |