Special linear Lie algebra

In mathematics, the special linear Lie algebra of order n (denoted ${\displaystyle {\mathfrak {sl}}_{n}(F)}$) is the Lie algebra of ${\displaystyle n\times n}$ matrices with trace zero and with the Lie bracket ${\displaystyle [X,Y]:=XY-YX}$. This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group.

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