Isomorphism classes of four dimensional nilpotent associative algebras over a field

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Abstract

In this paper we classify the isomorphism classes of four dimensional nilpotent associative algebras over a field F, studying regular subgroups of the affine group AGL4(F). In particular we provide explicit representatives for such classes when F is a finite field, the real field R or an algebraically closed field.
Original languageEnglish
Pages (from-to)132-160
Number of pages29
JournalLinear Algebra and Its Applications
DOIs
Publication statusPublished - 2017

Keywords

  • Algebra and Number Theory
  • Congruent matrices
  • Discrete Mathematics and Combinatorics
  • Finite field
  • Geometry and Topology
  • Nilpotent algebra
  • Numerical Analysis
  • Regular subgroup

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