Special Session 16

Algebras with Polynomial Identities

Organizers: Ana Vieira (Federal University of Minas Gerais, Brazil), Plamen Koshlukov (State University of Campinas, Brazil), Angela Valenti (University of Palermo, Italy)

MSC codes: 16R-XX

Description: The theory of algebras with polynomial identities (PI-algebras) studies associative—and also nonassociative—algebras that satisfy some nontrivial polynomial identity. Some obvious examples of polynomial identities are the commutativity or nilpotency conditions. This field combines algebraic and combinatorial methods, especially the action of the symmetric group on multilinear polynomial spaces, and the systematic usage of the theory of representations of the symmetric and the general linear groups. One employs asymptotic tools, such as the study of growth rates of invariant sequences associated with an algebra. These approaches make it possible to describe the structure of various classes of PI-algebras, classify varieties under specific conditions, and understand the asymptotic behavior of the growth of identities within the theory. In the last couple of decades, collaboration between researchers in Brazil and Italy in PI-theory has grown significantly. This period has been marked by strong academic exchange, frequent research visits, including many PhD students, and a substantial increase in joint scientific output. The integration between the two communities has played an important role in advancing the theory and in fostering new lines of investigation within the area.