denotes an exceptional Lie group and its associated Lie algebra, of rank two and dimension fourteen. Its roots form the G2 root system. The compact real form is the automorphism group of the octonion algebra; other real forms and the complex Lie algebra have the same complex root-system type.
On , take and . The special unitary group preserves the Kähler form by unitarity and preserves by its unit determinant. Fixing therefore embeds it in the compact G2 stabilizer of . The complexified seven-dimensional representation restricts as .
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In mathematics, "G2" can refer to several concepts depending on the context. Here are a couple of prominent interpretations: 1. **Lie Group G2**: In the context of algebraic and geometric structures, G2 is one of the five exceptional simple Lie groups. It has a dimension of 14 and is associated with a specific type of symmetry.