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searching for Cartan's criterion 2 found (13 total)

Casimir element (3,662 words) [view diff] exact match in snippet view article find links to article

abstract way—without using an explicit formula for the eigenvalue—using Cartan's criterion; see Sections 4.3 and 6.2 in the book of Humphreys. A Casimir element

Mutation (Jordan algebra) (15,817 words) [view diff] exact match in snippet view article

nondegeneracy of the Killing form is immediate from the explicit formula. By Cartan's criterion, g {\displaystyle {\mathfrak {g}}} is semisimple. In the next section