Faithful actions on Differential Graded Algebras determine the   isomorphism type of a large class of groups
  We prove that the isomorphism type of a large class of groups (containing finite groups, countable Artinian groups and mapping class groups of certain surfaces, among others) is determined by the set of differential graded $\mathbb Q$-algebras on which these groups act faithfully. 
Cristina Costoya 'and' Antonio Viruel
math.RT math.AT math.GT