Group gradings on triangularizable algebras

TL;DR

This paper classifies group gradings on triangularizable, infinite-dimensional algebras, revealing new structural insights by analyzing their topology and idempotent elements, thus advancing understanding in a relatively unexplored area.

Contribution

It provides a classification of group gradings on a class of non-simple, infinite-dimensional algebras, extending previous work to new algebraic structures.

Findings

Classification of group gradings on triangularizable algebras

Role of topology and idempotents in algebra structure

New insights into infinite-dimensional algebra gradings

Abstract

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.