References Intro to Lie Algebras by V. Kac

# Monthly Archives: November 2017

## Overview of Root System of Type E7

Lattice Roots Root count: Short Hand Notation and Rules where where , Basis High Root Poset of Abelian Radical Geometrically, Abelian Radical is the face of the Root polyhedron which contains (at long end of Dynkin graph) and is parallel to the hyperplane spanned by the remaining roots. Algebraically, it consists of roots which -coefficient… Read More »

## Motivation for Root Systems

Classification of Lattices Irreducibility and Root System A lattice is a configuration of evenly-spaced points in an ordinary Euclidean space such as that made by atoms (or molecules) distributed in a homogeneous solid. More precisely: A discrete collection of points is a lattice if a translation determined by any pair keeps the collection unchanged. The… Read More »

## E6 Overview

References Octonions

## E6 Abelian Radical Root Tree

Lattice Roots Root count: Basis Restriction from Extension from High Root Abelian Radical Geometrically, Abelian Radical is the face of the Root polyhedron which contains a long-leg extreme root in the Dynkin graph and is parallel to the hyperplane spanned by the remaining roots. Here we choose that end to be . Algebraically, it consists… Read More »