## 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:

**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 ...

... 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**...

**Simple Lie Group**s -

**Simple Lie Group**s

... 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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—Babette Deutsch (1895–1982)

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“How clean the sun when seen in its idea,

Washed in the remotest cleanliness of a heaven

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Let purple Phoebus *lie* in umber harvest,

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—Wallace Stevens (1879–1955)