Lectures on Quantum Groups by Olivier Schiffman, Pavel Etingof

By Olivier Schiffman, Pavel Etingof

Revised moment variation. The textual content covers the cloth provided for a graduate-level path on quantum teams at Harvard collage. The contents hide: Poisoon algebras and quantization, Poisson-Lie teams, coboundary Lie bialgebras, Drinfelds double development, Belavin-Drinfeld class, countless dimensional Lie bialgebras, Hopf algebras, Quantized common enveloping algebras, formal teams and h-formal teams, countless dimensional quantum teams, the quantum double, tensor different types and quasi Hopf-algebras, braided tensor different types, KZ equations and the Drinfeld classification, Quasi-Hpf enveloping algebras, Lie associators, Fiber functors and Tannaka-Driein duality, Quantization of finite Lie bialgebras, common buildings, common quantization, Dequantization and the equivalence theorem, KZ associator and a number of zeta capabilities, and Mondoromy of trigonometric KZ equations. Probems are given with each one topic and a solution secret's incorporated. desk of contents Poisson algebras and quantization Poisson-Lie teams Coboundary Lie bialgebras Drinfeld's double building Belavin-Drinfeld type (I) endless dimensional Lie bialgebras Belavin-Drinfeld category (II) Hopf algebras Quantized common enveloping algebras Formal teams and h-formal teams countless dimensional quantum teams The quantum double Tensor different types and quasi-Hopfalgebras Braided tensor different types KZ equations and the Drinfeld class Quasi-Hopf quantized enveloping algebras Lie associators Fiber functors and Tannaka-Krein duality Quantization of finite dimensional Lie bialgebras common structures common quantization Dequantization and the Equalivalence

Show description

Read Online or Download Lectures on Quantum Groups PDF

Similar algebra & trigonometry books

Homology of commutative rings

Unpublished MIT lecture notes

Rings, Extensions, and Cohomology

"Presenting the complaints of a convention held lately at Northwestern collage, Evanston, Illinois, at the party of the retirement of famous mathematician Daniel Zelinsky, this novel reference offers up to date insurance of issues in commutative and noncommutative ring extensions, specially these concerning problems with separability, Galois thought, and cohomology.

Basic Category Theory

On the center of this brief advent to classification thought is the belief of a common estate, very important all through arithmetic. After an introductory bankruptcy giving the elemental definitions, separate chapters clarify 3 ways of expressing common homes: through adjoint functors, representable functors, and bounds.

Additional info for Lectures on Quantum Groups

Example text

If N is a norm al s ubgro up o f G an d H is any s ubgro up of G, prove th at NHis a s ubgro up o f G. 4. Show th at the intersection o ftwo norm al s ubgro ups o f G is a norm al s ubgro up o f G. 5. If His a s ubgro up o f G an d Nis a norm al s ubgro up o f G, show th at H n Nis a norm als ub gro up o f H. 6. Show th at eve ry s ubgro up o f an abe li an gro up is norm al . * 7. Is the converse o f Problem 6 tr ue ? If yes , prove it, i f no, give an ex ample o f a non -abeli an gro up all o fwhose s ubgro ups ar enorm al .

Before we pro ceed with the proof it se lf it might be advi sa ble to see what it i s that we are going to prove. In part (a) we want to show that if two e el ment s e and fin G en joy the property that for every a E G, a = a e = e a = a · f = f · a, then e = f In part ( b) our aim i s to show that if x · a = a · x = e and y · a = a ·y = e, where a ll of a, x,y are in G, then X = y. • · 33 Sec. 3 35 Some Preliminary lemmas Problems I . In the following determine whether the systems described are groups.

Amongst mathematicians neither the beauty nor the significance of the first example which we have chosen to discuss-groups-is disputed. 1 Defi nition of a G ro u p At this juncture it is advisable to recall a situation discussed in the first chapter. For an arbitrary nonempty set S we defined A (S) to be the set of all one-to-one mappings of the set S onto itself. For any two elements a, T e A (S) we introduced a product, denoted by a o -r, and on further investi­ gation it turned out that the following facts were true for the elements of A (S) subject to this product : l .

Download PDF sample

Rated 4.61 of 5 – based on 37 votes