Splitting full matrix algebras over algebraic number fields

Gábor Ivanyos, L. Rónyai, Josef Schicho

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Let K be a fixed algebraic number field and let A be an associative algebra over K given by structure constants such that A≅Mn(K) holds for some positive integer n. Suppose that n is bounded. Then an isomorphism A→Mn(K) can be constructed by a polynomial time ff-algorithm. An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields. As a consequence, we obtain a polynomial time ff-algorithm to compute isomorphisms of central simple algebras of bounded degree over K.

Original languageEnglish
Pages (from-to)211-223
Number of pages13
JournalJournal of Algebra
Volume354
Issue number1
DOIs
Publication statusPublished - Mar 15 2012

Fingerprint

Algebraic number Field
Factoring
Matrix Algebra
Polynomial-time Algorithm
Isomorphism
Central Simple Algebra
Integer
Associative Algebra
Univariate
Galois field
Polynomial

Keywords

  • Central simple algebra
  • Lattice basis reduction
  • Maximal order
  • Minkowski's theorem on convex bodies
  • N-Descent on elliptic curves
  • Parametrization
  • Real and complex embedding
  • Severi-Brauer surfaces
  • Splitting
  • Splitting element

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Splitting full matrix algebras over algebraic number fields. / Ivanyos, Gábor; Rónyai, L.; Schicho, Josef.

In: Journal of Algebra, Vol. 354, No. 1, 15.03.2012, p. 211-223.

Research output: Contribution to journalArticle

Ivanyos, Gábor ; Rónyai, L. ; Schicho, Josef. / Splitting full matrix algebras over algebraic number fields. In: Journal of Algebra. 2012 ; Vol. 354, No. 1. pp. 211-223.
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