Isomorphism classes of four dimensional nilpotent associative algebras over a field

Marco Antonio Pellegrini

doi:10.1016/j.laa.2017.07.015

Isomorphism classes of four dimensional nilpotent associative algebras over a field

Marco Antonio Pellegrini

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	132-160
Number of pages	29
Journal	Linear Algebra and Its Applications
DOIs	https://doi.org/10.1016/j.laa.2017.07.015
Publication status	Published - 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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10.1016/j.laa.2017.07.015

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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.",

keywords = "Algebra and Number Theory, Congruent matrices, Discrete Mathematics and Combinatorics, Finite field, Geometry and Topology, Nilpotent algebra, Numerical Analysis, Regular subgroup, Algebra and Number Theory, Congruent matrices, Discrete Mathematics and Combinatorics, Finite field, Geometry and Topology, Nilpotent algebra, Numerical Analysis, Regular subgroup",

author = "Pellegrini, {Marco Antonio}",

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PY - 2017

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AB - 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.

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KW - Congruent matrices

KW - Discrete Mathematics and Combinatorics

KW - Finite field

KW - Geometry and Topology

KW - Nilpotent algebra

KW - Numerical Analysis

KW - Regular subgroup

KW - Algebra and Number Theory

KW - Congruent matrices

KW - Discrete Mathematics and Combinatorics

KW - Finite field

KW - Geometry and Topology

KW - Nilpotent algebra

KW - Numerical Analysis

KW - Regular subgroup

UR - http://hdl.handle.net/10807/105363

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DO - 10.1016/j.laa.2017.07.015

M3 - Article

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EP - 160

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Isomorphism classes of four dimensional nilpotent associative algebras over a field

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Keywords

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