# positive root

If $R\subset E$ is a root system, with $E$ an Euclidean vector space, then a subset $R^{+}\subset R$ is called a set of positive roots if there is a vector $v\in E$ such that $(\alpha,v)>0$ if $\alpha\in R^{+}$, and $(\alpha,v)<0$ if $\alpha\in R\backslash R^{+}$. http://planetmath.org/node/3645Roots which are not positive are called negative. Since $-\alpha$ is negative if and only if $\alpha$ is positive, exactly half the must be positive.

Title positive root PositiveRoot 2013-03-22 13:11:46 2013-03-22 13:11:46 mathwizard (128) mathwizard (128) 8 mathwizard (128) Definition msc 17B20 negative root