Germán García: Hom-associative structures in one-sided unital algebras

Abstract: Unitality in the usual sense is a very strict condition for hom-associative algebras to fulfill. Instead, a twisted hom-unitality condition is used, which equates to the twisting map being a multiplication operator. Frégier and Gohr proved that within any two-sided unital algebra exists a subalgebra which is in bijection with all twisting maps (all of which, multiplication operators) that make the product hom-associative. These elements are known as hom-associative structures.

In this talk I will extend this problem to one-sided unital algebras. First, I will discuss fundamental properties of hom-associativity in the one-sided unital setting and characterize multiplicativity in terms of the idempotents of the algebra. I will show a subspace of the algebra which contains all one-sided hom-unities, and use zero-division relations to find a subalgebra of hom-associative structures.

If time allows it, I will discuss some advancements in the non-unital version of this problem.