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E8 (mathematics) and List of simple Lie groups

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

Difference between E8 (mathematics) and List of simple Lie groups

E8 (mathematics) vs. List of simple Lie groups

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. In mathematics, the simple Lie groups were first classified by Wilhelm Killing and later perfected by Élie Cartan.

Similarities between E8 (mathematics) and List of simple Lie groups

E8 (mathematics) and List of simple Lie groups have 10 things in common (in Unionpedia): Élie Cartan, Dynkin diagram, Mathematics, Octonion, Real form (Lie theory), Simple group, Simple Lie group, Symmetric space, Theoretical physics, Triviality (mathematics).

Élie Cartan

Élie Joseph Cartan, ForMemRS (9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups and their geometric applications.

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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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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Octonion

In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.

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Real form (Lie theory)

In mathematics, the notion of a real form relates objects defined over the field of real and complex numbers.

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Simple group

In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.

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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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Symmetric space

In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point.

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Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.

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Triviality (mathematics)

In mathematics, the adjective trivial is frequently used for objects (for example, groups or topological spaces) that have a very simple structure.

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The list above answers the following questions

E8 (mathematics) and List of simple Lie groups Comparison

E8 (mathematics) has 120 relations, while List of simple Lie groups has 24. As they have in common 10, the Jaccard index is 6.94% = 10 / (120 + 24).

References

This article shows the relationship between E8 (mathematics) and List of simple Lie groups. To access each article from which the information was extracted, please visit:

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