Abstract

Locally semisimple algebras (LS-algebras) are inductive limits of semisimple algebras, and can be fully characterized by their Bratteli diagrams ($\mathbb{N}$-graded graphs). (Finite) harmonic functions on Bratteli diagrams are a standard tool in the representation theory of LS-algebras and semifinite harmonic functions are a natural generalization. We plan to give an overview of the subject, starting with the classical results for the infinite symmetric group, followed by the recent results for the infinite symmetric inverse semigroup. Joint work with N.Safonkin.