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单词 SimpleRoot
释义

simple root


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vector spaceMathworldPlanetmath

Let RE be a root systemMathworldPlanetmath, 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 combinationMathworldPlanetmath 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 groupMathworldPlanetmathPlanetmath of the root system acts simply transitively on the set of bases.

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更新时间:2025/5/5 2:19:24