# simple root

Let $R\subseteq E$ be a root system^{}, with $E$ a Euclidean vector space (http://planetmath.org/VectorSpace). If ${R}^{+}$ is a set of
positive roots, then a root is called simple if it is positive, and not the sum of any two
positive roots. The simple roots form a basis of the vector space $E$, and any positive root
is a positive integer linear combination^{} of simple roots.

A set of roots which is simple with respect to some choice of a set of positive roots is called a
base. The Weyl group^{} of the root system acts simply transitively on the set of bases.

Title | simple root |
---|---|

Canonical name | SimpleRoot |

Date of creation | 2013-03-22 13:11:49 |

Last modified on | 2013-03-22 13:11:49 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 6 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 17B20 |

Defines | base |