Octonion example sentences

"Octonion" Example Sentences

1. The octonion algebra is a non-associative algebra.
2. Octonions are also known as Cayley numbers.
3. The octonion multiplication table has 480 entries.
4. Octonion multiplication is neither commutative nor associative.
5. The octonion algebra is an eight-dimensional vector space over the real numbers.
6. Some physicists have suggested using octonions to describe the fundamental forces of nature.
7. John Baez has written extensively about the properties of octonions.
8. Octonions can be used to describe rotations in seven dimensions.
9. The octonion algebra is the largest of the four normed division algebras.
10. Octonions were first introduced by John T. Graves in 1843.
11. The octonion norm is not positive definite.
12. Octonions have applications in string theory and other areas of theoretical physics.
13. The octonion algebra is a composition algebra.
14. Octonions can be used to construct a non-associative Lie algebra.
15. Octonions can be represented as 2x2 matrices over the quaternion algebra.
16. Octonions have a unique division algebra structure.
17. Octonions have been used to study exceptional Lie groups.
18. The octonion algebra is sometimes described as a non-associative normed division algebra.
19. Octonions have been used to study the spinor representation of the Lorentz group.
20. Octonions can be used to construct a non-associative Jordan algebra.
21. Octonions have properties similar to those of the quaternions.
22. Octonions have been used to study supersymmetry in theoretical physics.
23. Octonions have been used to study the Hodge conjecture in algebraic geometry.
24. Octonions have been used to study the exceptional isomorphism E8≅SO(16).
25. Octonions have been used to study integrable systems.
26. Octonions have been used to study the octonionic projective plane.
27. Octonions have been used to study the Hopf fibration.
28. Octonions have been used to study quaternionic geometry.
29. Octonions have been used to study relativistic quantum mechanics.
30. Octonions have been used to study non-commutative geometry.

Common Phrases

1. Octonion algebra is a non-commutative extension of quaternion algebra;
2. Octonions have eight dimensions and are often used in mathematical physics;
3. The real part of an octonion is a scalar, while the imaginary part is a seven-dimensional vector;
4. Octonions have a unique algebraic structure known as the division algebra;
5. The multiplication of octonions is not associative, unlike quaternion multiplication;
6. Octonions have connections to the exceptional Lie groups and F4-Dynkin diagram;
7. Octonions have applications in string theory, M-theory, and other areas of physics and mathematics.