Some remarks on symmetric linear functions and pseudotrace maps

Abstract

Let $A$ be a finite-dimensional associative algebra and $\phi$ a symmetric linear function on $A$. In this note, we will show that the pseudotrace maps defined in [6] are obtained as special cases of well-known symmetric linear functions on the endomorphism rings of projective modules. As an application of our approach, we will give proofs of several propositions and theorems in [6] for an arbitrary finite-dimensional associative algebra.