### Abstract

Let K be an algebraic number field of degree d and discriminant Δ over ℚ. Let A be an associative algebra over K given by structure constants such that A ≅ M_{n}(K) holds for some positive integer n. Suppose that d, n and |Δ| are bounded. In a previous paper, a polynomial time ff-algorithm was given to construct explicitly an isomorphism A → M_{n}(K). Here we simplify and improve this algorithm in the cases n ≤ 43, K=ℚ and n=2 with K=ℚ(√-3) or The improvements are based on work by Y. Kitaoka and R. Coulangeon on tensor products of lattices.

Original language | English |
---|---|

Pages (from-to) | 141-156 |

Number of pages | 16 |

Journal | JP Journal of Algebra, Number Theory and Applications |

Volume | 28 |

Issue number | 2 |

Publication status | Published - Mar 2013 |

### Fingerprint

### Keywords

- Bergé-Martinet constant
- Central simple algebra
- Hermite constant
- Lattice basis reduction
- Maximal order
- Real and complex embedding
- Tensor product of lattices

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*JP Journal of Algebra, Number Theory and Applications*,

*28*(2), 141-156.

**Improved algorithms for splitting full matrix algebras.** / Ivanyos, Gábor; Lelkes, Ádám D.; Rónyai, L.

Research output: Contribution to journal › Article

*JP Journal of Algebra, Number Theory and Applications*, vol. 28, no. 2, pp. 141-156.

}

TY - JOUR

T1 - Improved algorithms for splitting full matrix algebras

AU - Ivanyos, Gábor

AU - Lelkes, Ádám D.

AU - Rónyai, L.

PY - 2013/3

Y1 - 2013/3

N2 - Let K be an algebraic number field of degree d and discriminant Δ over ℚ. 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 d, n and |Δ| are bounded. In a previous paper, a polynomial time ff-algorithm was given to construct explicitly an isomorphism A → Mn(K). Here we simplify and improve this algorithm in the cases n ≤ 43, K=ℚ and n=2 with K=ℚ(√-3) or The improvements are based on work by Y. Kitaoka and R. Coulangeon on tensor products of lattices.

AB - Let K be an algebraic number field of degree d and discriminant Δ over ℚ. 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 d, n and |Δ| are bounded. In a previous paper, a polynomial time ff-algorithm was given to construct explicitly an isomorphism A → Mn(K). Here we simplify and improve this algorithm in the cases n ≤ 43, K=ℚ and n=2 with K=ℚ(√-3) or The improvements are based on work by Y. Kitaoka and R. Coulangeon on tensor products of lattices.

KW - Bergé-Martinet constant

KW - Central simple algebra

KW - Hermite constant

KW - Lattice basis reduction

KW - Maximal order

KW - Real and complex embedding

KW - Tensor product of lattices

UR - http://www.scopus.com/inward/record.url?scp=84875542521&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875542521&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84875542521

VL - 28

SP - 141

EP - 156

JO - JP Journal of Algebra, Number Theory and Applications

JF - JP Journal of Algebra, Number Theory and Applications

SN - 0972-5555

IS - 2

ER -