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.
Pellegrini, M. A., Isomorphism classes of four dimensional nilpotent associative algebras over a field, <<LINEAR ALGEBRA AND ITS APPLICATIONS>>, 2017; (533): 132-160. [doi:10.1016/j.laa.2017.07.015] [http://hdl.handle.net/10807/105363]
Isomorphism classes of four dimensional nilpotent associative algebras over a field
Pellegrini, Marco AntonioPrimo
2017
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.
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