Orthogonal symmetric Lie algebra

In mathematics, an orthogonal symmetric Lie algebra is a pair ( g , s ) {\displaystyle ({\mathfrak {g}},s)} consisting of a real Lie algebra g {\displaystyle {\mathfrak {g}}} and an automorphism s {\displaystyle s} of g {\displaystyle {\mathfrak {g}}} of order 2 {\displaystyle 2} such that the eigenspace u {\displaystyle {\mathfrak {u}}} of s corresponding to 1 (i.e., the set u {\displaystyle {\mathfrak {u}}} of fixed points) is a compact subalgebra. If "compactness" is omitted, it is called a symmetric Lie algebra.

Source: Wikipedia — Orthogonal symmetric Lie algebra (CC BY-SA 4.0)

Orthogonal symmetric Lie algebra

In mathematics, an orthogonal symmetric Lie algebra is a pair ( g , s ) {\displaystyle ({\mathfrak {g}},s)} consisting of a real Lie algebra g {\displaystyle {\mathfrak {g}}} and an automorphism s {\displaystyle s} of g {\displaystyle {\mathfrak {g}}} of order 2 {\displaystyle 2} such that the eigenspace u {\displaystyle {\mathfrak {u}}} of s corresponding to 1 (i.e., the set u {\displaystyle {\mathfrak {u}}} of fixed points) is a compact subalgebra. If "compactness" is omitted, it is called a symmetric Lie algebra.

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Source: Wikipedia "Orthogonal symmetric Lie algebra" · CC BY-SA 4.0

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