Semi-simplicity
Alberto Ibort, Miguel Rodríguez · 2019
This chapter addresses the study of the structure of the algebra of a groupoid and shows that the groupoid algebra is semi-simple, hence, it decomposes as direct sum of simple algebras. It studies the structure of subrepresentations of direct sums of irreducible representations and discusses transitivity properties of representations. The chapter discusses the characterizations of semisimplicity and presents a theorem to prove that the algebra of a finite groupoid is semi-simple.