In this paper we highlight the connection between certain classes of regular subgroups of the affine group AGLn(F), F a field, and associative nilpotent F-algebras of dimension n. We also describe how the classification of projective congruence classes of square matrices is equivalent to the classification of regular subgroups of particular shape.
Pellegrini, M. A., Regular subgroups, nilpotent algebras and projectively congruent matrices, <<INTERNATIONAL JOURNAL OF GROUP THEORY>>, 2018; 7 (1): 51-56. [doi:10.22108/ijgt.2017.21215] [http://hdl.handle.net/10807/111453]
Regular subgroups, nilpotent algebras and projectively congruent matrices
Pellegrini
Primo
2018
Abstract
In this paper we highlight the connection between certain classes of regular subgroups of the affine group AGLn(F), F a field, and associative nilpotent F-algebras of dimension n. We also describe how the classification of projective congruence classes of square matrices is equivalent to the classification of regular subgroups of particular shape.
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