[[Lie algebra]]
# Classical Lie algebra

The **classical Lie algebras** are:[^1972] #m/def/lie

- [[Special linear Lie algebra|$A_n = \mathfrak{sl}_{n+1}\mathbb{K}$]]
- [[Orthogonal Lie algebra|$B_{n} = \mathfrak{o}_{2n+1}\mathbb{K}$]]
- [[Symplectic Lie algebra|$C_{n} = \mathfrak{sp}_{2n}\mathbb{K}$]]
- [[Orthogonal Lie algebra|$D_{n} = \mathfrak{o}_{2n}\mathbb{K}$]] 

  [^1972]: 1972\. [[Sources/@humphreysIntroductionLieAlgebras1972|Introduction to Lie Algebras and Representation Theory]], §1.2, pp. 2–3

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