Below you will find example sentences with "connected lie". The examples show how this phrase is used in real sentences and which words often surround it.
Connected Lie in a sentence
About this phrase
- Belongs to the word: lie
Example types with connected lie
Below, the examples are grouped by length and sentence type:
Thus, compact connected Lie groups have been completely classified. (9 words)
Moreover, every homomorphism between Lie algebras lifts to a unique homomorphism between the corresponding simply connected Lie groups. (18 words)
Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to covering ( Lie's third theorem ). (27 words)
The universal cover of any connected Lie group is a simply connected Lie group, and conversely any connected Lie group is a quotient of a simply connected Lie group by a discrete normal subgroup of the center. (37 words)
It is a connected Lie group of dimension 2n 2 + n. *The group of invertible upper triangular n by n matrices is a solvable Lie group of dimension n(n + 1)/2. (32 words)
As for classification, it can be shown that any connected Lie group with a given Lie algebra is isomorphic to the universal cover mod a discrete central subgroup. (28 words)
Example sentences (6)
The universal cover of any connected Lie group is a simply connected Lie group, and conversely any connected Lie group is a quotient of a simply connected Lie group by a discrete normal subgroup of the center.
Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to covering ( Lie's third theorem ).
As for classification, it can be shown that any connected Lie group with a given Lie algebra is isomorphic to the universal cover mod a discrete central subgroup.
It is a connected Lie group of dimension 2n 2 + n. *The group of invertible upper triangular n by n matrices is a solvable Lie group of dimension n(n + 1)/2.
Moreover, every homomorphism between Lie algebras lifts to a unique homomorphism between the corresponding simply connected Lie groups.
Thus, compact connected Lie groups have been completely classified.