On a class of self-injective locally bounded categories (Q1818022)

The repetitive category \(\widehat{A}\) of a finite-dimensional algebra \(A\) is a well-known example of a self-injective locally bounded category. Factoring out the Nakayama automorphism one gets back a finite-dimensional algebra \(T(A)\), the trivial extension of \(A\). It is shown in the present paper that conversely any such category, which in addition is triangular (= directed) and has no indecomposable projective module of length smaller than 3, arises as the repetitive category of some finite-dimensional algebra which then also is triangular.