This paper is a new contribution to the study of regular subgroups of the affine group AGLn(F), for any field F. In particular we associate to each partition λ≠(1^{n+1}) of n+1 abelian regular subgroups in such a way that different partitions define non-conjugate subgroups. Moreover, we classify the regular subgroups of certain natural types for n≤4. Our classification is equivalent to the classification of split local algebras of dimension n+1 over F. Our methods, based on classical results of linear algebra, are computer free.
Pellegrini, M. A., Tamburini Bellani, M. C., More on regular subgroups of the affine group, <<LINEAR ALGEBRA AND ITS APPLICATIONS>>, 2016; (505): 126-151. [doi:10.1016/j.laa.2016.04.031] [http://hdl.handle.net/10807/77764]
More on regular subgroups of the affine group
Pellegrini, Marco AntonioPrimo
;Tamburini Bellani, Maria ClaraUltimo
2016
Abstract
This paper is a new contribution to the study of regular subgroups of the affine group AGLn(F), for any field F. In particular we associate to each partition λ≠(1^{n+1}) of n+1 abelian regular subgroups in such a way that different partitions define non-conjugate subgroups. Moreover, we classify the regular subgroups of certain natural types for n≤4. Our classification is equivalent to the classification of split local algebras of dimension n+1 over F. Our methods, based on classical results of linear algebra, are computer free.
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