Induced Representations of Lie Algebras. Ii
نویسندگان
چکیده
1. Introduction. Let © be a Lie algebra over a field A. A decomposition of © is a triple (ni, b, n2) of subalgebras of © such that ® = niffif)©n2 a vector space direct sum and such that [b, n,-]Cn< for 4 = 1, 2. In [5] we showed how one could "induce" ©-modules from b-modules in a natural manner. In this paper we prove a useable necessary and sufficient condition that a ©-module must satisfy in order that it be "induced" from an b-module. We apply this method of induction to obtain all well-known simple modules (not necessarily finite dimensional) for semisimple Lie algebras over algebraically closed fields of characteristic 0.
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