Abstract:
In this work, we present the classification of non-associative algebras, focusing on
three main classes: Leibniz algebras, Jordan algebras, and genetic algebras. The aim is
to classify these algebras in low dimensions, considering that complexity increases as the
dimension grows. Over the field of complex numbers, we will address the classification
of Leibniz algebras, particularly Lie algebras, of dimension at most three, based on [4],
and genetic algebras of dimension up to two, following [16]. Finally, over an arbitrary
field of characteristic different from two, we discuss the classification of Jordan algebras
of dimension at most two, using [5] as a reference.
