Abelian Lie group information

In geometry, an abelian Lie group is a Lie group that is an abelian group. A connected abelian real Lie group is isomorphic to R k × ( S 1 ) h {\displaystyle...

classification of Lie groups. Analogously to abelian, nilpotent, and solvable groups, one can define abelian, nilpotent, and solvable Lie algebras. A Lie algebra...

mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does...

simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can be...

1-dimensional compact, connected Lie group. Moreover, every n {\displaystyle n} -dimensional compact, connected, abelian Lie group is isomorphic to T n {\displaystyle...

group; and whether or not they are simply connected) as well as on their algebraic properties (abelian; simple; semisimple). For more examples of Lie...

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same...

Milne, J. S., Affine Group Schemes; Lie Algebras; Lie Groups; Reductive Groups; Arithmetic Subgroups Mumford, David (1970), Abelian varieties, Oxford University...

simple connected Lie groups. Gsol/Gnil is abelian. A connected abelian Lie group is isomorphic to a product of copies of R and the circle group S1. Gnil/1 is...

nilpotent group is a group that is "almost abelian". This idea is motivated by the fact that nilpotent groups are solvable, and for finite nilpotent groups, two...

theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For example, the group of integers (equipped...

cyclic group. An abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements...

mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points...

example would be any abelian Lie group. This is because any such group is a nilpotent Lie group. For example, one can take the group of real numbers under...

families of non-abelian finite simple groups may be considered to be of Lie type. One of 16 families of groups of Lie type The Tits group is generally considered...

the classification of abelian groups: according to the fundamental theorem of finite abelian groups, every finite abelian group can be expressed as the...

groups and free Lie algebras. The group (Z,+) of integers is free of rank 1; a generating set is S = {1}. The integers are also a free abelian group,...

The modular group may be realised as a quotient of the special linear group SL(2, Z). If n ≥ 2, then the group GL(n, F) is not abelian. If V is a vector...

specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently...

Free abelian group Free group Free product Generating set of a group Group cohomology Group extension Presentation of a group Product of group subsets...

also an example of a compact abelian Lie group. This follows from the fact that the unit circle is a compact abelian Lie group (when identified with the...

isomorphic to the additive group of Z/nZ, the integers modulo n. Every cyclic group is an abelian group (meaning that its group operation is commutative)...

algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by...