Computation of isotopisms of algebras over finite fields by means of graph invariants

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic. In order to illustrate th...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2017-07, Vol.318, p.307-315
Main Authors: Falcón, O.J., Falcón, R.M., Núñez, J., Pacheco, A.M., Villar, M.T.
Format: Article
Language:English
Subjects:
Finite field
Graph theory
Isomorphism
Latin square
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Summary:In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic. In order to illustrate their efficiency, we determine explicitly the classification of two- and three-dimensional partial quasigroup rings.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.09.002