Lie groups, algebraic groups and lattices

TL;DR

This paper provides an introductory overview of Lie groups, algebraic groups, and their discrete subgroups, based on lecture series from a 2011 summer school, aiming to familiarize readers with fundamental concepts and structures.

Contribution

It offers a concise, accessible introduction to the theories of Lie and algebraic groups and their lattices, synthesizing key ideas from a series of lectures.

Findings

Clarifies the basic structures of Lie and algebraic groups

Explains the role of discrete subgroups and lattices

Provides foundational knowledge for further study

Abstract

This is a brief introduction to the theories of Lie groups, algebraic groups and their discrete subgroups, which is based on a lecture series given during the Summer School held in the Banach Centre in Poland in Summer 2011.