simple root

\\PMlinkescapephrase

vector space

Let $R\\subseteq E$ be a root system, with $E$ a Euclidean vector space (http://planetmath.org/VectorSpace). If $R^{+}$ is a set ofpositive roots, then a root is called simple if it is positive, and not the sum of any twopositive roots. The simple roots form a basis of the vector space $E$ , and any positive rootis 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 abase. The Weyl group of the root system acts simply transitively on the set of bases.

单词	SimpleRoot
释义	simple root \\PMlinkescapephrase vector space Let $R\\subseteq E$ be a root system, with $E$ a Euclidean vector space (http://planetmath.org/VectorSpace). If $R^{+}$ is a set ofpositive roots, then a root is called simple if it is positive, and not the sum of any twopositive roots. The simple roots form a basis of the vector space $E$ , and any positive rootis 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 abase. The Weyl group of the root system acts simply transitively on the set of bases.
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