lema de Schur
Lemma stating that a module homomorphism between two simple modules over the same ring is either an isomorphism or identically zero
In mathematics, Schur's lemma is an elementary but useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations of a group G and φ is a linear map from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0.
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lema de Schur
Lemma stating that a module homomorphism between two simple modules over the same ring is either an isomorphism or identically zero
In mathematics, Schur's lemma is an elementary but useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations of a group G and φ is a linear map from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0.
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In mathematics, Schur's lemma is an elementary but useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations of a group G and φ is a linear map from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0. An important special case occurs when M = N, i.e. φ is a self-map; in particular, for representations over an algebraically closed field (e.g. C {\displaystyle \mathbb {C} } ), any element of the center of a group must act as a scalar operator (a scalar multiple of the identity) on M. The lemma is named after Issai Schur who used it to prove the Schur orthogonality relations and develop the basics of the representation theory of finite groups. Schur's lemma admits generalisations to Lie groups and Lie algebras, the most common of which are due to Jacques Dixmier and Daniel Quillen.
Texto: Wikipédia em inglês, CC BY-SA 4.0. ·
