Computing explicit isomorphisms with full matrix algebras over $\mathbb{F}_q(x)$

Gábor Ivanyos; Péter Kutas; Lajos Rónyai

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arXiv · 1508.07755

Computing explicit isomorphisms with full matrix algebras over $\mathbb{F}_q(x)$

Gábor Ivanyos·Péter Kutas·Lajos Rónyai

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Abstract

We propose a polynomial time $f$-algorithm (a deterministic algorithm which uses an oracle for factoring univariate polynomials over $\mathbb{F}_q$) for computing an isomorphism (if there is any) of a finite dimensional $\mathbb{F}_q(x)$-algebra $A$ given by structure constants with the algebra of $n$ by $n$ matrices with entries from $\mathbb{F}_q(x)$. The method is based on computing a finite $\mathbb{F}_q$-subalgebra of $A$ which is the intersection of a maximal $\mathbb{F}_q[x]$-order and a maximal $R$-order, where $R$ is the subring of $\mathbb{F}_q(x)$ consisting of fractions of polynomials with denominator having degree not less than that of the numerator.

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BibTeX RIS

Gábor Ivanyos, Péter Kutas, Lajos Rónyai. 2017-01-02. Computing explicit isomorphisms with full matrix algebras over $\mathbb{F}_q(x)$. https://arxiv.org/abs/1508.07755

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