Counting Finite-Dimensional Algebras Over Finite Field

Nikolaas Verhulst

doi:10.1007/s00025-020-01281-6

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Counting Finite-Dimensional Algebras Over Finite Field

Nikolaas Verhulst

Year: 2020 Journal: Results in Mathematics Vol: 75 (4) Publisher: Birkhäuser

DOI: 10.1007/s00025-020-01281-6

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Abstract

Abstract In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed, finite dimension over a given finite field. We show how this method works in the case of 2-dimensional algebras over the field $${\mathbb {F}}_{2}$$ F 2 .

Keywords:

Dimension (graph theory) Mathematics Field (mathematics) Finite field Pure mathematics Discrete mathematics Algebra over a field

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Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Matrix Theory and Algorithms

Physical Sciences → Computer Science → Computational Theory and Mathematics

Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

Counting Finite-Dimensional Algebras Over Finite Field

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