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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Some articles on simple lie group:
... 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 ...
... 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 ...
... 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 ...
... 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 ...
... 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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