Common · Knowledge
G2 (mathematics)
Simple Lie group; the automorphism group of the octonions
In mathematics, G2 is three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g 2 , {\displaystyle {\mathfrak {g}}_{2},} as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14.
From Wikipedia
In mathematics, G2 is three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g 2 , {\displaystyle {\mathfrak {g}}_{2},} as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has two fundamental representations, with dimension 7 and 14. The compact form of G2 can be described as the automorphism group of the octonion algebra or, equivalently, as the subgroup of SO(7) that preserves any chosen particular vector in its 8-dimensional real spinor representation (a spin representation).
Text: Wikipédia, CC BY-SA 4.0. · Image: User:Hagman (CC BY-SA 3.0) ·
Related cards
-
★★
Octonion
Non-commutative, non-associative algebra of numbers with eight real components
-
★
F4 (mathematics)
52-dimensional exceptional simple Lie group
-
★★
Point groups in two dimensions
Geometry concept
-
★★★
Lie group
Group that is also a smooth manifold with group operations that are smooth
-
★★★
Lie algebra
Vector space with an alternating binary operation satisfying the Jacobi identity.
-
★★
SL2(R)
Group of real 2×2 matrices with unit determinant