Commutators example sentences

"Commutators" Example Sentences

1. The commutators of a group measure how non-commutative the group is.
2. The commutators of two elements in a group give information about how they interact.
3. The Lie bracket of a Lie algebra is defined in terms of commutators.
4. Commutators are used to study the structure of groups and algebras.
5. The commutator subgroup of a group is a normal subgroup that measures how non-Abelian the group is.
6. The commutators of a matrix group can be used to determine whether the group is solvable or not.
7. Commutators are also used in quantum mechanics to describe the uncertainty in the position and momentum of a particle.
8. The commutators of a Lie algebra form a Lie subalgebra.
9. Commutators are important in the study of automorphisms of groups.
10. The commutator of two operators in quantum mechanics measures how much they fail to commute.
11. The Jacobi identity for commutators expresses the fact that the Lie bracket is associative.
12. Commutators of elements in a group can be used to define a new group, called the derived group.
13. Commutators are also used in tensor products to measure the extent to which the product is non-commutative.
14. Commutators are important in the study of Lie groups and Lie algebras.
15. The commutators of a Lie algebra determine its structure up to isomorphism.
16. Commutators are used in the classification of finite simple groups.
17. The commutator length of a group measures how many commutators are needed to generate all elements of the group.
18. Commutators are used in the definition of Jordan algebras.
19. The centralizer of an element in a group is the set of elements that commute with it, except for commutators.
20. The commutators of elements of a Lie group can be used to define a new Lie algebra, called the Lie algebra of the group.
21. Commutators are used in the definition of enveloping algebras of Lie algebras.
22. The commutators of a group determine its second homology group.
23. Commutators are used in the study of automorphisms of Lie algebras.
24. The commutators of a group can be used to determine whether it is perfect or not.
25. Commutators are important in the study of Kac-Moody algebras.
26. The group generated by the commutators of two elements in a group is called the commutator subgroup of the group.
27. Commutators are used in the definition of semisimple algebras.
28. The commutators of two isometries in a metric space can be used to define the distortion of the space.
29. Commutators are used in the proof of the Poincaré-Birkhoff-Witt theorem.
30. The commutators of elements in a group can be used to define a new group, called the Verbal subgroup.

Common Phrases

1. The commutators in this circuit need to be properly aligned.
2. The technician used a commutator to switch between different modes.
3. The commutators on the old generator were causing it to malfunction.
4. The commutator brush needs to be replaced to improve performance.
5. The commutators in the motor were not synced correctly.
6. The engineer discovered a faulty commutator during the inspection.
7. We need to check the commutator connections before starting the machine.
8. The commutator bar was damaged, causing electrical issues.
9. The commutator ring was coated with a layer of insulation for safety reasons.
10. The operation of the machine requires a high-quality commutator.