# A geometric approach to classical Lie algebras

**Datum:**21 april 2017

**Locatie:**UAntwerpen, Campus Middelheim, G.005 - Middelheimlaan 1 - 2020 Antwerpen (route: UAntwerpen, Campus Middelheim)

**Tijdstip:**14 - 15 uur

**Korte beschrijving:**Seminar by Hans Cuypers

**About the seminar**

There exist strong connections between classical Lie algebras and algebraic groups and algebraic groups and buildings. In this talk we discuss a direct connection between classical Lie algebras and buildings. We use this connection to give a characterization of (most of) the classical Lie algebras as (simple) Lie algebras generated by extremal elements. (An extremal element $x$ in a Lie algebra $L$ has the property that $[x,[x,L]]$ is $1$-dimensional and spanned by $x$.)

**Url:**https://www.uantwerpen.be/en/rg/fundamental-mathematics/