## Abstract

Let B be an algebra over a field, Ã a subalgebra of $, and CL an equivalence class of finite dimensional irreducible Ã-modules. Under certain restrictions, bisections are established between the set of equivalence classes of irreducible a-modules containing a nonzero a-primary B-submodule, and the sets of equivalence classes of all irreducible modules of certain canonically constructed algebras. Related results had been obtained by Harish-Chandra and R. Godement in special cases. The general methods and results appear to be useful in the representation theory of semisimple Lie groups. enveloping algebra, Po in care-Birkhoff-Witt theorem, simple ring, full matrix algebra.

Original language | English (US) |
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Pages (from-to) | 45-57 |

Number of pages | 13 |

Journal | Transactions of the American Mathematical Society |

Volume | 176 |

DOIs | |

State | Published - Feb 1973 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- Applied Mathematics

## Keywords

- Absolutely irreducible module
- Extension of submodules
- Finitely semisimple module
- Irreducible module
- Irreducible representation
- Lie algebra
- Primary submodule
- Universal