Abstract: This chapter discusses the representations of Lie algebras. Representation spaces of equivalent representations have the same dimensions. Representations are understood to be linear representations. A basic problem of the representation theory of Lie algebras is to find all the representations (up to equivalence) of a Lie algebra. A representation ρ of g is said to be irreducible if the representation space V is irreducible under ρ(g). Otherwise, ρ is said to be reducible. If a representation ρ of g is reducible, then the representation space contains a proper invariant subspace V1. If ρ is the direct sum of some irreducible representations, then it is said to be completely reducible. Invariant subspaces of the regular representation are ideals of g. If g is semisimple, then the regular representation is completely reducible.
Publication Year: 1975
Publication Date: 1975-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 2
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