  Classifying isomorphism classes of group gradings on algebras presents a
compelling challenge, particularly within the realms of non-simple and
infinite-dimensional algebras, which have been relatively unexplored. This
study focuses on a kind of algebra that is neither simple nor
finite-dimensional, aiming to classify the group gradings on triangularizable
algebras as defined by Mesyan in 2019. The topology of infinite-dimensional
algebras, along with the role of idempotent elements, plays a crucial role in
our findings, leading to new insights and a deeper understanding of their
structure.
