# Lectures on Quantum Groups

@inproceedings{Etingof2001LecturesOQ, title={Lectures on Quantum Groups}, author={Pavel Etingof and Olivier Schiffmann}, year={2001} }

Revised second edition. The text covers the material presented for a graduate-level course on quantum groups at Harvard University. Covered topics include: Poisson algebras and quantization, Poisson-Lie groups, coboundary Lie bialgebras, Drinfelds double construction, Belavin-Drinfeld classification, Infinite dimensional Lie bialgebras, Hopf algebras, Quantized universal enveloping algebras, formal groups and h-formal groups, infinite dimensional quantum groups, the quantum double, tensor…

## 418 Citations

Quantum groups, character varieties and integrable systems

- Mathematics
- 2017

Author(s): Schrader, Gus Knight | Advisor(s): Reshetikhin, Nicolai | Abstract: In this thesis we address several questions involving quantum groups, quantum cluster algebras, and integrable systems,…

Quantum Groups and Quantum Cohomology

- Mathematics
- 2012

In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q,…

Quantum Divided Power Algebra, Q-Derivatives, and Some New Quantum Groups

- Mathematics
- 2000

Abstract The discussions in the present paper arise from exploring intrinsically the structural nature of the quantum n-space. A kind of braided category G B of Λ-graded θ-commutative associative…

Complex Semisimple Quantum Groups and Representation Theory

- Mathematics
- 2020

This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is…

Belavin-Drinfeld cohomologies and introduction to classification of quantum groups

- Mathematics
- 2014

In the present article we discuss the classification of quantum groups whose quasiclassical limit is a given simple complex Lie algebra g. This problem reduces to the classification of all Lie…

Poisson orders on large quantum groups

- Mathematics
- 2020

We bring forward the notions of large quantum groups and their relatives. The starting point is the concept of distinguished pre-Nichols algebra arXiv:1405.6681 belonging to a one-parameter family;…

Introduction to double Hecke algebras

- Mathematics
- 2004

This paper is based on the introduction to the monograph ``Double affine Hecke algebras'' to be published by Cambridge University Press. The connections with Knizhnik-Zamolodchikov equations,…

Lectures on q-analogues of Cartan domains and associated Harish-Chandra modules

- Mathematics
- 2001

This volume contains a mildly expanded version of lectures and talks at seminars and conferences, as well as review papers on subjects listed in the title of the volume. A great deal of these texts…

Classification of Quantum Groups via Galois Cohomology

- MathematicsCommunications in Mathematical Physics
- 2019

The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Kulish et al. (J Soviet Math 23:2435–2441, 1983), they found a new algebra which was later called…