Talk:Schur's lemma

Schur lemma for simple modules

Is the Schur lemma mentioned on Simple module the same as the one here? MarSch 16:45, 7 Apr 2005 (UTC)

The simple answer is 'yes'. Charles Matthews 17:39, 7 Apr 2005 (UTC)

Schur's lemma in differential geometry

In differential geometry, Schur's Lemma usually refers to the result that if the sectional curvature of a Riemannian manifold does not depend on the choice of 2-plane in any tangent space, then it also does not depend on the point in the manifold, i.e., the manifold has constant curvature. Shouldn't this be added here? 128.138.64.92 21:13, 10 April 2007 (UTC)

Matrix form

Given a matrix representation does the following hold or not? (ir)reducible matrix <=> (ir)reducible representation

Where can I find a (concise?) proof of schur's lemma in matrix form? — Preceding unsigned comment added by 157.193.2.37 (talk) 00:07, 15 August 2011 (UTC)

$\operatorname {End} _{A}M=k$

"This holds more generally for any algebra R over an algebraically closed field k and for any simple module M that is at most countably-dimensional: the only linear transformations of M that commute with all transformations coming from R are scalar multiples of the identity."

This is not true without the additional assumption that k is uncountable. Counterexample: the algebra of rational functions over a countable algebraically closed field, considered as a module over itself. AlexShamov (talk) 09:13, 30 October 2015 (UTC)