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En (Lie algebra)

Index 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. [1]

21 relations: Affine Lie algebra, Cartan matrix, Dynkin diagram, E6 (mathematics), E7 (mathematics), E8 (mathematics), E8 lattice, F4 (mathematics), G2 (mathematics), Heisenberg group, International Conference on Differential Geometric Methods in Theoretical Physics, Kac–Moody algebra, Lie algebra, Lorentz group, M-theory, Mathematics, Nilradical of a Lie algebra, Uniform 1 k2 polytope, Uniform 2 k1 polytope, Uniform k 21 polytope, Unimodular lattice.

Affine Lie algebra

In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra.

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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.

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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 (mathematics)

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.

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E8 lattice

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

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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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Heisenberg group

In mathematics, the Heisenberg group H, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form \end under the operation of matrix multiplication.

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International Conference on Differential Geometric Methods in Theoretical Physics

International Conference on Differential Geometric Methods in Theoretical Physics are congresses held every few years on the subject of Differential geometric methods in Theoretical physics.

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Kac–Moody algebra

In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently discovered them) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix.

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Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

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Lorentz group

In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (nongravitational) physical phenomena.

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M-theory

M-theory is a theory in physics that unifies all consistent versions of superstring theory.

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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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Nilradical of a Lie algebra

In algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible.

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Uniform 1 k2 polytope

In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.

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Uniform 2 k1 polytope

In geometry, 2k1 polytope is a uniform polytope in n dimensions (n.

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Uniform k 21 polytope

In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular polytope facets.

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Unimodular lattice

In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1.

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Redirects here:

E10 (Lie algebra), E10 (mathematics), E11 (mathematics), E9 (Lie algebra), E9 (mathematics), En (mathematics).

References

[1] https://en.wikipedia.org/wiki/En_(Lie_algebra)

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