Examples of 'lie group' in a sentence
Meaning of "lie group"
lie group - in mathematics, a Lie group is a group that is also a smooth manifold, with smooth multiplication and inverse operations. It has applications in various branches of mathematics and physics
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- Any group that is a smooth manifold and whose group operations are differentiable.
How to use "lie group" in a sentence
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lie group
Lie group of invertible linear transformations.
As part of some larger lie group.
Lie group theory.
Now think about representations of a Lie group.
Lie group representation.
The set of unitriangular matrices forms a Lie group.
Every Lie group is a parallelizable manifold.
A simpler example would be any abelian Lie group.
It is a Lie group action if it is differentiable.
It is a ten dimensional noncompact Lie group.
It is an example of a Lie group because it has the structure of a manifold.
Continuous symmetries are mathematically represented by Lie group actions.
In the compact Lie group case he proved a fundamental character formula.
On the automorphism group of a Lie group.
In the theory of Lie group decompositions it is generalized by the Iwasawa decomposition.
See also
Transformation with regard to a Lie group.
The quotient of a Lie group by a closed normal subgroup is a Lie group.
Then can be given the structure of a Lie group.
The Lie group that it generates is the special linear group.
The notion is closely related to that of a representation of a Lie group.
The fundamental group of a connected Lie group is always commutative.
The orthogonal group also forms an interesting example of a Lie group.
Subsequently the name homotopy Lie group has also been used.
This is because any such group is a nilpotent Lie group.
The Lorentz group is a Lie group of symmetries of the spacetime of special relativity.
It is a compact connected Lie group.
The Lie group can be thought of as the group of symmetries of the geometry.
The proof given below assumes a matrix Lie group.
It is a Lie group if K is the real or complex field or quaternions.
It is also important to know the center of a connected compact Lie group.
This example shows that a solvable Lie group need not be unimodular.
We have a more concrete definition in the case of a matrix Lie group.
Any Lie group gives rise to a Lie algebra.
Evidently the group of units of the ring of dual quaternions is a Lie group.
Consider the Lie group inclusion.
The corresponding irreducible representations are the fundamental representations of the Lie group.
That HT is a Lie group can be seen directly in this case.
They can often be represented as the quotient of a Lie group by a compact subgroup.
Let be a Lie group over and its Lie algebra.
Each of these surfaces of constant curvature has a transitive Lie group of symmetries.
Associated with any Lie group is the Lie algebra of group generators.
Any finite group may be given the structure of a complex Lie group.
It is a Lie group.
It seems that something deep is happening with nilpotent element in a Lie group.
A Cartan subgroup of a compact connected Lie group is a maximal connected Abelian subgroup a maximal torus.
This relation is becoming clear in the case of a real reductive Lie group Go.
The Lie group.
Here are some important examples in which unitary representations of a Lie group have been analyzed.
Real Lie group.
The Möbius group is then a complex Lie group.
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