Exhaustive construction of four-dimensional unital division algebras over finite fields with Kleinian automorphism group

Mashhour Al Ali Bani-Ata

doi:10.1007/s13366-018-0407-5

Exhaustive construction of four-dimensional unital division algebras over finite fields with Kleinian automorphism group

Mashhour Al Ali Bani-Ata

Public Authority for Applied Education and Training

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

Abstract

The purpose of this paper is to give an exhaustive construction of the four-dimensional unital division algebras A over finite fields F _q , q is an odd prime, admitting an elementary abelian four-group of automorphisms E≤ Aut(A) , using tools from algebraic geometry.

Original language	English
Pages (from-to)	111-122
Number of pages	12
Journal	Beitrage zur Algebra und Geometrie
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/s13366-018-0407-5
State	Published - 12 Mar 2019

Keywords

Chevalley–Warning theorem
Division algebra
Homogeneous polynomials

Funding Agency

Kuwait Foundation for the Advancement of Sciences

Access to Document

10.1007/s13366-018-0407-5

Cite this

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title = "Exhaustive construction of four-dimensional unital division algebras over finite fields with Kleinian automorphism group",

abstract = " The purpose of this paper is to give an exhaustive construction of the four-dimensional unital division algebras A over finite fields F q , q is an odd prime, admitting an elementary abelian four-group of automorphisms E≤ Aut(A) , using tools from algebraic geometry.",

keywords = "Chevalley–Warning theorem, Division algebra, Homogeneous polynomials",

author = "Bani-Ata, \{Mashhour Al Ali\}",

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year = "2019",

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doi = "10.1007/s13366-018-0407-5",

language = "English",

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AU - Bani-Ata, Mashhour Al Ali

PY - 2019/3/12

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N2 - The purpose of this paper is to give an exhaustive construction of the four-dimensional unital division algebras A over finite fields F q , q is an odd prime, admitting an elementary abelian four-group of automorphisms E≤ Aut(A) , using tools from algebraic geometry.

AB - The purpose of this paper is to give an exhaustive construction of the four-dimensional unital division algebras A over finite fields F q , q is an odd prime, admitting an elementary abelian four-group of automorphisms E≤ Aut(A) , using tools from algebraic geometry.

KW - Chevalley–Warning theorem

KW - Division algebra

KW - Homogeneous polynomials

UR - https://www.scopus.com/pages/publications/85061899357

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DO - 10.1007/s13366-018-0407-5

M3 - Article

AN - SCOPUS:85061899357

SN - 0138-4821

VL - 60

SP - 111

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JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

IS - 1

ER -

Exhaustive construction of four-dimensional unital division algebras over finite fields with Kleinian automorphism group

Abstract

Keywords

Funding Agency

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