A brief introduction to quantum groups

TL;DR

This paper provides an overview of the fundamental concepts and aspects of quantum groups, serving as lecture notes for educational purposes and offering a broad introduction to the subject.

Contribution

It offers a comprehensive, accessible introduction to quantum groups, synthesizing lecture content and expanding on foundational ideas for new learners.

Findings

Summarizes key concepts of quantum groups

Provides educational insights and lecture-based explanations

Serves as a foundational resource for further study

Abstract

These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the CMSA Math Science Literature Lecture Series in May 2020. We attempt to give a bird's-eye view of basic aspects of the theory of quantum groups.