Let L be a finite dimensional Lie algebra. Any finite dimensional representation of L is completely reducible. Show that L must be semisimple. (converse to Weyl's Theorem)
Let L be a finite dimensional Lie algebra. Any finite dimensional representation of L is completely reducible. Show that L must be semisimple. (converse to Weyl's Theorem)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.2: Complex Numbers And Quaternions
Problem 50E
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Let L be a finite dimensional Lie algebra. Any finite dimensional representation of L is completely reducible. Show that L must be semisimple. (converse to Weyl's Theorem)
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