Weyl's theorem on complete reducibility

Target entity: Weyl's theorem on complete reducibility
Context triple: [Lie algebra, hasKeyResult, Weyl's theorem on complete reducibility]

• A. Peter–Weyl theorem
  The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
• B. Harish-Chandra regularity theorem
  The Harish-Chandra regularity theorem is a fundamental result in representation theory that asserts characters of irreducible admissible representations of real reductive Lie groups are given by real-analytic, locally integrable functions on the group.
• C. Borel–Weil theorem
  The Borel–Weil theorem is a fundamental result in representation theory that realizes irreducible representations of compact Lie groups as spaces of holomorphic sections of line bundles over their flag manifolds.
• D. Schur’s lemma
  Schur’s lemma is a fundamental result in representation theory stating that any homomorphism between irreducible representations is either zero or an isomorphism, and that endomorphisms of an irreducible representation over an algebraically closed field are scalar multiples of the identity.
• E. Maschke’s theorem
  Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Weyl's theorem on complete reducibility
Target entity description: Weyl's theorem on complete reducibility is a fundamental result in the representation theory of semisimple Lie algebras stating that every finite-dimensional representation decomposes into a direct sum of irreducible subrepresentations.

• A. Peter–Weyl theorem
  The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
• B. Harish-Chandra regularity theorem
  The Harish-Chandra regularity theorem is a fundamental result in representation theory that asserts characters of irreducible admissible representations of real reductive Lie groups are given by real-analytic, locally integrable functions on the group.
• C. Borel–Weil theorem
  The Borel–Weil theorem is a fundamental result in representation theory that realizes irreducible representations of compact Lie groups as spaces of holomorphic sections of line bundles over their flag manifolds.
• D. Schur’s lemma
  Schur’s lemma is a fundamental result in representation theory stating that any homomorphism between irreducible representations is either zero or an isomorphism, and that endomorphisms of an irreducible representation over an algebraically closed field are scalar multiples of the identity.
• E. Maschke’s theorem
  Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
• F. None of above. chosen