Algebraic groups | Exceptional Lie algebras | Lie groups | Octonions

G2 (mathematics)

In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras 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). (Wikipedia).

G2 (mathematics)
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GT2. Definition of Subgroup

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From playlist Abstract Algebra

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From playlist Music Lessons

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Chapter 4 - Solving Linear Equations with Technology - IB Math Studies (Math SL)

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From playlist IB Math Studies Chapter 4

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Group Theory: The Center of a Group G is a Subgroup of G Proof

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From playlist Abstract Algebra

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Equivalence Relation on a Group Two Proofs

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From playlist Abstract Algebra

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Example of Group: GL(2, R) (3 of 3)

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From playlist Abstract Algebra

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SAT Math (Geometry) - Practice 3.8

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From playlist SAT Math Practice

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From playlist Graph Theory (Discrete Math)

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Block diagram algebra 2019-04-15

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From playlist Discrete

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From playlist Daniel Rubin Show, Full episodes

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Tutorial for Simon Caron-huot lectures by Yue-Zhou Li

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From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology (ONLINE) - 2022

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An Oxford Mathematics Graduate Supervision - Geometry and Physics in 7 Dimensions

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From playlist Oxford Mathematics Student Tutorials and Graduate Supervisions

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8. g(2) for atoms and light

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From playlist MIT 8.422 Atomic and Optical Physics II, Spring 2013

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From playlist Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry

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From playlist Discrete Math 2

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From playlist MATH1011 Calculus Problems

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Pre-recorded lecture 22: Open problems (part 2)

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From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)

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Huajie Chen - Convergence of the Planewave Approximations for Quantum Incommensurate Systems

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From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics

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Lorenzo Foscolo: ALC manifolds with exceptional holonomy

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From playlist Geometry

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What is a Subgraph? | Graph Theory

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From playlist Graph Theory

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Weyl character formula | Group representation | Lie group | Dynkin diagram | Linear span | Real representation | Vector space | Finite field | Holonomy | Index of a subgroup | Spin representation | Simple Lie group | Élie Cartan | Spinor | Root system | Simple group | Cartan matrix | Janko group J1 | Dihedral group | Mathematics | Coxeter group | G2 manifold | Octonion | Seven-dimensional cross product | Weyl group | Leonard Eugene Dickson | Lie algebra | Cuboctahedron | Manifold | Automorphism group | Algebraic group | G2-structure | Ree group | Fundamental representation | Distribution (differential geometry) | Outer automorphism group