Coxeter–Dynkin diagram and E8 (mathematics)

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Coxeter–Dynkin diagram and E8 (mathematics)

Coxeter–Dynkin diagram vs. E8 (mathematics)

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes). In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8.

Similarities between Coxeter–Dynkin diagram and E8 (mathematics)

Coxeter–Dynkin diagram and E8 (mathematics) have 10 things in common (in Unionpedia): Cartan matrix, Dynkin diagram, E6 (mathematics), E7 (mathematics), E8 lattice, En (Lie algebra), F4 (mathematics), G2 (mathematics), Root system, Simple Lie group.

Cartan matrix

In mathematics, the term Cartan matrix has three meanings.

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Dynkin diagram

In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line).

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E6 (mathematics)

In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.

Coxeter–Dynkin diagram and E6 (mathematics) · E6 (mathematics) and E8 (mathematics) · See more »

E7 (mathematics)

In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7.

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E8 lattice

In mathematics, the E8 lattice is a special lattice in R8.

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En (Lie algebra)

In mathematics, especially in Lie theory, En is the Kac–Moody algebra whose Dynkin diagram is a bifurcating graph with three branches of length 1,2, and k, with k.

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F4 (mathematics)

In mathematics, F4 is the name of a Lie group and also its Lie algebra f4.

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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 \mathfrak_2, as well as some algebraic groups.

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Root system

In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties.

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Simple Lie group

In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.

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The list above answers the following questions

What Coxeter–Dynkin diagram and E8 (mathematics) have in common
What are the similarities between Coxeter–Dynkin diagram and E8 (mathematics)

Coxeter–Dynkin diagram and E8 (mathematics) Comparison

Coxeter–Dynkin diagram has 117 relations, while E8 (mathematics) has 120. As they have in common 10, the Jaccard index is 4.22% = 10 / (117 + 120).

References

This article shows the relationship between Coxeter–Dynkin diagram and E8 (mathematics). To access each article from which the information was extracted, please visit:

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