nLab special linear Lie algebra

Idea,

For $k$ a field and $n$ a natural number, the special linear Lie algebra $\mathfrak{sl}(n,k)$ is the Lie algebra of trace-free $n\times n$-matrices with entries in $k$, with Lie bracket being the commutator of matrix multiplication.

Examples

• sl(2)

Related concepts

• special linear group

• special unitary Lie algebra

• special orthogonal Lie algebra

• Lie algebra weight system

Literature

• Jean-Pierre Serre: Representations of $\mathfrak{sl}_n$, Chapter VII of: Lie Algebras and Lie Groups – 1964 Lectures given at Harvard University, Lecture Notes in Mathematics 1500, Springer (1992) [doi:10.1007/978-3-540-70634-2]