Mathematicians Map Lie Group

Beauty of Mathematics

clipped from www.sciencedaily.com Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E8. the E8 calculation is an investigation of symmetry. Mathematicians invented the Lie groups to capture the essence of symmetry: underlying any symmetrical object, such as a sphere, is a Lie group. The ways that E8 manifests itself as a symmetry group are called representations. The goal is to describe all the possible representations of E8. The new result is a complete list of these building blocks for the representations of E8, and a precise description of the relations between them, all encoded in a matrix with 205,263,363,600 entries. we physicists have come to appreciate its exceptional role only more recently --- yet, in our attempts to unify gravity with the other fundamental forces into a consistent theory of quantum gravity, we now encounter it at almost every corner! Beautiful Symmetry E8 itself is 248-dimensional!