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arXiv · 1106.6191

Splitting full matrix algebras over algebraic number fields

Gábor Ivanyos·Lajos Rónyai·Josef Schicho
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Abstract

Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(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.

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Gábor Ivanyos, Lajos Rónyai, Josef Schicho. 2011-12-21. Splitting full matrix algebras over algebraic number fields. https://arxiv.org/abs/1106.6191

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