Projective Essential Idempotents

This paper introduces the concept of projective essential idempotents. These are primitive central idempotents in a twisted group algebra. The first main result provides conditions for the existence of them. In the second main result, we prove that every q-ary simplex code can be seen as an ideal of a twisted group algebra generated by a projective essential idempotent. We conclude by describing a decoding process using projective essential idempotents.