$E$-symmetric algebras I

We study various symmetry conditions related to the Auslander-Reiten formula for finite-dimensional algebras. In particular, we define a new class of algebras which we call $E$-symmetric. A theorem by Derksen-Weyman-Zelevinksy implies that all Jacobian algebras are $E$-symmetric. We prove the converse for the class of monomial algebras.