Splitting full matrix algebras over algebraic number fields

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 deter...

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Bibliographic Details
Published in:	Journal of algebra Vol. 354; no. 1; pp. 211 - 223
Main Authors:	Ivanyos, Gábor, Rónyai, Lajos, Schicho, Josef
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.03.2012
Subjects:	Central simple algebra Lattice basis reduction Maximal order Minkowskiʼs theorem on convex bodies n-Descent on elliptic curves Parametrization Real and complex embedding Severi–Brauer surfaces Splitting Splitting element Parametrization Splitting Central simple algebra Splitting element Real and complex embedding Minkowskiʼs theorem on convex bodies Lattice basis reduction n-Descent on elliptic curves Severi–Brauer surfaces Maximal order
ISSN:	0021-8693, 1090-266X
Online Access:	Get full text
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Summary:	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.
ISSN:	0021-8693 1090-266X
DOI:	10.1016/j.jalgebra.2012.01.008