Lattice-theoretical aspects of evolution algebras

Abstract: Lattice theories have been developed in several algebraic structures, such as groups and Lie algebras; however, this is not the case for evolution algebras, which are commutative but nonassociative structures introduced by Tian and Vojtěchovský in 2006 to model non-Mendelian inheritance. Motivated by this, in this talk we study the subalgebra lattices of solvable evolution algebras, focusing on two classical lattice-theoretical properties: distributivity and modularity. Subsequently, we turn to maximal subalgebras, whose intersection is traditionally known as the Frattini subalgebra. This resulting Frattini theory allows us to investigate intrinsic properties and to characterise dually atomistic evolution algebras.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar