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Schur's Lemma

There are at least two statements known as Schur's lemma.

1. The endomorphism ring of an irreducible module is a division algebra.

2. Let V, W be irreducible (linear) G-spaces and A:V->W a G-linear map. Then A is either invertible or A=0 (Hsiang 2000, p. 3).

See also

Division Algebra, Endomorphism Ring, Schur's Representation Lemma

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References

Herstein, I. N. Topics in Algebra, 2nd ed. New York: Springer-Verlag, 1975.Hsiang, W. Y. Lectures on Lie Groups. Singapore: World Scientific, p. 3, 2000.

Referenced on Wolfram|Alpha

Schur's Lemma

Cite this as:

Weisstein, Eric W. "Schur's Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchursLemma.html

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