Simple Lie

Some articles on lie, simple lie, simple:

Glossary Of Semisimple Groups - S
... Semisimple Lie algebra Semisimple Lie group Simple Lie algebra Simple Lie group Simple root Simply laced group A simple Lie group is simply laced when its Dynkin diagram is ...
Types of Lie Groups and Structure Theory
... Lie groups are classified according to their algebraic properties (simple, semisimple, solvable, nilpotent, abelian), their connectedness (connected or simply connected) and their compactness ... Compact Lie groups are all known they are finite central quotients of a product of copies of the circle group S1 and simple compact Lie groups (which ... Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible ...
E8 (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 ... designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7 ... Wilhelm Killing (1888, 1888, 1889, 1890) discovered the complex Lie algebra E8 during his classification of simple compact Lie algebras, though he did not prove its existence, which ...
Simple Lie Group - Method of Classification
... Such groups are classified using the prior classification of the complex simple Lie algebras for which see the page on root systems ... It is shown that a simple Lie group has a simple Lie algebra that will occur on the list given there, once it is complexified (that is, made into a complex vector space rather than a real one) ...
Symmetric Spaces in General - Classification Results
... of Riemannian symmetric spaces does not extend readily to the general case for the simple reason that there is no general splitting of a symmetric space ... Here a symmetric space G/H with Lie algebra is said to be irreducible if is an irreducible representation of ... The latter question is more subtle than in the Riemannian case even if is simple, G/H might not be irreducible ...

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