Improved algorithms for splitting full matrix algebras

Gábor Ivanyos, Ádám D. Lelkes, L. Rónyai

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 ≅ 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.

Original languageEnglish
Pages (from-to)141-156
Number of pages16
JournalJP Journal of Algebra, Number Theory and Applications
Volume28
Issue number2
Publication statusPublished - Mar 2013

Fingerprint

Algebraic number Field
Associative Algebra
Matrix Algebra
Discriminant
Tensor Product
Polynomial-time Algorithm
Isomorphism
Simplify
Integer

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

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

In: JP Journal of Algebra, Number Theory and Applications, Vol. 28, No. 2, 03.2013, p. 141-156.

Research output: Contribution to journalArticle

Ivanyos, Gábor ; Lelkes, Ádám D. ; Rónyai, L. / Improved algorithms for splitting full matrix algebras. In: JP Journal of Algebra, Number Theory and Applications. 2013 ; Vol. 28, No. 2. pp. 141-156.
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