A Borel subalgebra of a finite-dimensional complex Lie algebra is a maximal solvable subalgebra. In a semisimple Lie
algebra, all Borel subalgebras are conjugate. For 
, the upper triangular trace-zero matrices form a Borel
subalgebra.
Borel Subalgebra
See also
Lie Algebra, Semisimple Lie Algebra, Solvable Lie AlgebraExplore with Wolfram|Alpha
References
Humphreys, J. E. Introduction to Lie Algebras and Representation Theory. New York: Springer-Verlag, 1972.Cite this as:
Weisstein, Eric W. "Borel Subalgebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BorelSubalgebra.html