Summary of contents: representations of a Lie algebras; representation spaces and dimension of a representation; examples of representations; homomorphism and isomorphism of representations; trivial and adjoint representations; faithful representations; direct sum and tensor product representations; invariant subspaces, reducible and irreducible representations; highest weights; Killing form associated to a representation; Casimir operator; proof that the Casimir operator commutes with the representation; Schur's lemma; worked examples; automorphism group; representation of Lie groups; Adjoint representation.
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Lecture Notes for this lecture:
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