nLab Nathan Jacobson

Nathan Jacobson was an American algebraist.

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Jacobson radicals are named after him.

Proposition

(Jacobson’s lemma) If $A$ and $B$ are matrices over a field of characteristic 0 and $A$ commutes with $A B - B A$ then $A B - B A$ is nilpotent.

Selected writing

Proving what came to be called the Jacobson-Morozov theorem:

• Nathan Jacobson: Completely reducible Lie algebras of linear transformations, Proc. Amer. Math. Soc. 2 (1951) 105-113 [doi:10.1090/S0002-9939-1951-0049882-5]

On Lie algebras:

• Nathan Jacobson: Lie Algebras, Dover Books (1979) [ISBN:9780486638324]

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