Isotopisms of Lie algebras

Abstract

The distribution of algebras into equivalence classes is usually done according to the concept of isomorphism. However, such a distribution can also be done into isotopism classes. The concept of isotopism was explicitly introduced in 1942 by Abraham Adrian Albert to classify non-associative algebras. In this poster we deal with the study of isotopisms of Lie algebras. The reasons for using both criteria, isotopisms and isomorphisms, to classify Lie algebras is due to that classifications by isotopisms are different from those by isomorphisms, which involves obtaining new information about these algebras. On a sake of example, we indicate some recent results obtained by ourselves, which are related to the distribution into isomorphism and isotopism classes of filiform Lie algebras over finite fields.