Finding maximal orders in semisimple algebras over Q

Gábor Ivanyos, Lajos Rónyai

Research output: Contribution to journalArticle

24 Citations (Scopus)

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 languageEnglish
Pages (from-to)245-261
Number of pages17
JournalComputational Complexity
Volume3
Issue number3
DOIs
Publication statusPublished - 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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