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Special Linear Lie Algebra

The special linear Lie algebra sl_n(F) over a field F is the Lie algebra of n×n matrices of matrix trace zero, with Lie bracket

[X,Y]=XY-YX.

It is the Lie algebra of the special linear group SL_n(F). Over a field of characteristic 0, sl_n(F) has dimension n^2-1 and is simple for n>=2.

See also

Lie Algebra, Simple Lie Algebra, Special Linear Group

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References

Humphreys, J. E. Introduction to Lie Algebras and Representation Theory. New York: Springer-Verlag, 1972.

Cite this as:

Weisstein, Eric W. "Special Linear Lie Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SpecialLinearLieAlgebra.html

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