# What is simple lie group?

## 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.

### Some articles on simple lie group:

Simple Lie Group - Simply Laced Groups
... A simply laced group is a Lie group whose Dynkin diagram only contain simple links, and therefore all the nonzero roots of the corresponding Lie algebra have the same length ... The A, D and E series groups are all simply laced, but no group of type B, C, F, or G is simply laced ...
Classification of Riemannian Symmetric Spaces - Classification Scheme
... G is a (real) simple Lie group B ... G is either the product of a compact simple Lie group with itself (compact type), or a complexification of such a Lie group (non-compact type) ... The examples in class B are completely described by the classification of simple Lie groups ...
Wess–Zumino–Witten Model - Action - Topological Obstructions
... They are maps from flat 3-space into the Lie group G ... However, the homotopy group π3(G) = Z for any compact, connected simple Lie group G ... that coupling constant k must be an integer when G is a connected, compact, simple Lie group ...
List Of Simple Lie Groups - Simple Lie Groups
... is no generally accepted definition of a simple Lie group, and in particular it is not necessarily defined as a Lie group that is simple as an abstract group ... Authors differ on whether a simple Lie group has to be connected, or on whether it is allowed to have a non-trivial center, or on whether R is a simple Lie group ... The most common definition implies that simple Lie groups must be connected, and non-abelian, but are allowed to have a non-trivial center ...
Lie - Religious Perspectives - In Zoroastrianism
... universe Asha, which is truth, order and that which is real, and Druj, which is "the Lie" ... Later on the Lie became personified as Angra Mainyu, a figure similar to the Christian Devil, who was portrayed as the eternal opponent of Ahura Mazda (God) ...

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