E8: Exceptional Simple Lie Groups

Sophus Lie (19th-century Norwegian mathematician) discovered Lie groups – sets of continuous transformation that leave an object unchanged in appearence.

Example: rotate sphere around any axis, the sphere looks exactly the same.

Later mathematicians found 5 exceptions to the 4 classes of Lie groups that Lie knew about. (Why only 5 ?)

The most complicated of the “exceptional simple Lie groups” is E8. It describes the symmetries of a 57-dimensional object that can in essence be repeated in 248 ways without changing its appearance.

To understand using E8 in all its possibilities requires calculation of 200 billion numbers.

E8 is the Lie group underlying some Superstring theories that physicists are pursuing in an effort to tie gravity and the other fundamental forces of the universe into one theory.

E8 could be determining the inner structure of the universe.

Note: Other examples of Physics taking advantage of Abstract math:
Newton invented Calculus to study the motion of planets.

Fourier Analysis, the mathmatics of periodic patterns, proved essential in studying phenomena like light waves.

■ Physicists have employed Lie groups in Quantum Mechanics and Relativity.


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