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See Table of Lie groups for a list. General linear group, special linear group. SL 2 (R) SL 2 (C) Unitary group, special unitary group. SU(2) SU(3) Orthogonal group, special orthogonal group. Rotation group SO(3) SO(8) Generalized orthogonal group, generalized special orthogonal group. The special unitary group SU(1,1) is the unit sphere in the ...
Note that a "complex Lie group" is defined as a complex analytic manifold that is also a group whose multiplication and inversion are each given by a holomorphic map. The dimensions in the table below are dimensions over C. Note that every complex Lie group/algebra can also be viewed as a real Lie group/algebra of twice the dimension.
A real Lie group is a group that is also a finite-dimensional real smooth manifold, in which the group operations of multiplication and inversion are smooth maps. Smoothness of the group multiplication : (,) = means that μ is a smooth mapping of the product manifold G × G into G. The two requirements can be combined to the single requirement ...
Aside from that, it’s a great mystery game where one player – who can’t talk at all – uses clues to guide the good players to a player, weapon, and item at the table that was used to ...
Pages in category "Lie groups" The following 164 pages are in this category, out of 164 total. ... Table of Lie groups; Tangent Lie group; Theory of Lie groups; Theta ...
Once these are known, the ones with non-trivial center are easy to list as follows. Any simple Lie group with trivial center has a universal cover whose center is the fundamental group of the simple Lie group. The corresponding simple Lie groups with non-trivial center can be obtained as quotients of this universal cover by a subgroup of the ...
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3. simply laced group (a simple Lie group is simply laced when its Dynkin diagram is without multiple edges). 4. simple root. A subset of a root system is called a set of simple roots if it satisfies the following conditions: is a linear basis of .
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