### Abstract

We consider the algorithmic problem of constructing a maximal order in a semisimple algebra over an algebraic number field. A polynomial time ff-algorithm is presented to solve the problem. (An ffalgorithm is a deterministic method which is allowed to call oracles for factoring integers and for factoring polynomials over finite fields. The cost of a call is the size of the input given to the oracle.) As an application, we give a method to compute the degrees of the irreducible representations over an algebraic number field K of a finite group G, in time polynomial in the discriminant of the defining polynomial of K and the size of a multiplication table of G.

Original language | English |
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Pages (from-to) | 245-261 |

Number of pages | 17 |

Journal | Computational Complexity |

Volume | 3 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1 1993 |

### Keywords

- Subject classifications: 68Q40, 11Y40, 68Q25, 11Y16

### ASJC Scopus subject areas

- Theoretical Computer Science
- Mathematics(all)
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

Ivanyos, G., & Rónyai, L. (1993). Finding maximal orders in semisimple algebras over Q.

*Computational Complexity*,*3*(3), 245-261. https://doi.org/10.1007/BF01271370